\begin{thebibliography}{82}
\providecommand{\natexlab}[1]{#1}
\providecommand{\url}[1]{\texttt{#1}}
\expandafter\ifx\csname urlstyle\endcsname\relax
  \providecommand{\doi}[1]{doi: #1}\else
  \providecommand{\doi}{doi: \begingroup \urlstyle{rm}\Url}\fi

\bibitem[Arveson(1976)]{Arveson}
W.~Arveson.
\newblock \emph{An Invitation to C*-Algebra}.
\newblock Graduate Texts in Mathematics. Springer-Verlag, New York, 1976.

\bibitem[Baier et~al.(2003)Baier, Haverkort, Hermanns, and
  Katoen]{Baier+Haverkort+Hermanns+Katoen}
C.~Baier, B.~Haverkort, H.~Hermanns, and J.-P. Katoen.
\newblock Model-checking algorithms for continuous time {M}arkov chains.
\newblock \emph{IEEE Trans. Softw. Eng.}, 29\penalty0 (6):\penalty0 524~--~541,
  June 2003.

\bibitem[Barr and Wells(1999)]{Barr+Wells}
M.~Barr and C.~Wells.
\newblock \emph{Category Theory for Computing Science}.
\newblock Les Publications CRM, Montreal, 1999.

\bibitem[Bauer(1968)]{Bauer}
H.~Bauer.
\newblock \emph{{Wahrscheinlichkeitstheorie und Grundz{\"u}ge der
  Ma{\ss}theorie}}.
\newblock Walter de Gruyter, Berlin, 1968.

\bibitem[Billingsley(1968)]{Billingsley-alt}
P.~Billingsley.
\newblock \emph{Convergence of Probability Measures}.
\newblock John Wiley \& Sons, New York, 1st edition, 1968.

\bibitem[Billingsley(1999)]{Billingsley-neu}
P.~Billingsley.
\newblock \emph{Convergence of Probability Measures}.
\newblock John Wiley \& Sons, New York, 2nd edition, 1999.

\bibitem[Blackburn et~al.(2001)Blackburn, de~Rjike, and
  Venema]{Blackburn-Rijke-Venema}
P.~Blackburn, M.~de~Rjike, and Y.~Venema.
\newblock \emph{Modal Logic}.
\newblock Number~53 in Cambridge Tracts in Theoretical Computer Science.
  Cambridge University Press, Cambridge, UK, 2001.

\bibitem[Blackburn et~al.(2007)Blackburn, van Benthem, and
  Wolter]{CollectionModalLogic}
P.~Blackburn, J.~van Benthem, and F.~Wolter, editors.
\newblock \emph{Handbook of Modal Logic}, volume~3 of \emph{Studies in Logic
  and Practical Reasoning}.
\newblock Elsevier, Amsterdam, 2007.

\bibitem[Bonsangue and Kurz(2005)]{Bonsangue-Kurz}
M.~M. Bonsangue and A.~Kurz.
\newblock Duality of logics of transition systems.
\newblock In V.~Sassone, editor, \emph{Proc. FOSSACS'05}, volume 3441 of
  \emph{LNCS}, pages 455--469, 2005.

\bibitem[Borceux(1994{\natexlab{a}})]{Borceux-1}
F.~Borceux.
\newblock \emph{Handbook of Categorical Algebra 1: Basic Category Theory},
  volume~50 of \emph{Encyclopedia of Mathematics and its Applications}.
\newblock Cambridge University Press, Cambridge, UK, 1994{\natexlab{a}}.

\bibitem[Borceux(1994{\natexlab{b}})]{Borceux-2}
F.~Borceux.
\newblock \emph{Handbook of Categorical Algebra 2: Categories and Structures},
  volume~51 of \emph{Encyclopedia of Mathematics and its Applications}.
\newblock Cambridge University Press, Cambridge, UK, 1994{\natexlab{b}}.

\bibitem[Burris and Sankappanavar(1981)]{Burris-UnivAlgebra}
S.~Burris and H.~P. Sankappanavar.
\newblock \emph{A Course in Universal Algebra}.
\newblock Springer-Verlag (The Millenium Edition), 1981.

\bibitem[Castaing and Valadier(1977)]{Castaing-Valadier}
C.~Castaing and M.~Valadier.
\newblock \emph{Convex Analysis and Measurable Multifunctions}.
\newblock Number 580 in Lect. Notes Math. Springer-Verlag, Berlin, Heidelberg,
  New York, 1977.

\bibitem[C{\^\i}rstea and Pattinson(2004)]{Cirstea-Pattinson}
C.~C{\^\i}rstea and D.~Pattinson.
\newblock Modular construction on modal logics.
\newblock In P.~Gardner and N.~Yoshida, editors, \emph{Proc. CONCUR'04}, number
  3170 in Lect. Notes Comp. Sci., pages 258~--~275, 2004.

\bibitem[Clarke et~al.(1999)Clarke, Grumberg, and Peled]{Clarke-Grumberg-Peled}
E.~M. Clarke, O.~Grumberg, and D.~A. Peled.
\newblock \emph{Model Checking}.
\newblock The MIT Press, Cambridge, MA, 1999.

\bibitem[Danos et~al.(2006)Danos, Desharnais, Laviolette, and
  Panangaden]{Danos-etal-Cocongruences}
V.~Danos, J.~Desharnais, F.~Laviolette, and P.~Panangaden.
\newblock Bisimulation and cocongruence for probabilistic systems.
\newblock \emph{Information and Computation}, 204\penalty0 (4):\penalty0
  503--523, 2006.

\bibitem[Desharnais and Panangaden(2003)]{Desharnais-Panangaden-ContTime}
J.~Desharnais and P.~Panangaden.
\newblock Continuous stochastic logic characterizes bisimulation of
  continuous-time {M}arkov processes.
\newblock \emph{J. Log. Alg. Programming}, 56\penalty0 (1-2):\penalty0
  99~--~115, 2003.

\bibitem[Desharnais et~al.(2002)Desharnais, Edalat, and
  Panangaden]{Desharnais-Edalat-Panangaden}
J.~Desharnais, A.~Edalat, and P.~Panangaden.
\newblock Bisimulation of labelled {M}arkov-processes.
\newblock \emph{Information and Computation}, 179\penalty0 (2):\penalty0
  163~--~193, 2002.

\bibitem[Doberkat(2006{\natexlab{a}})]{EED-Algebras}
E.-E. Doberkat.
\newblock {E}ilenberg-{M}oore algebras for stochastic relations.
\newblock \emph{Information and Computation}, 204:\penalty0 1756 -- 1781,
  2006{\natexlab{a}}.

\bibitem[Doberkat(2005{\natexlab{a}})]{EED-Analytic}
E.-E. Doberkat.
\newblock Semi-pullbacks for stochastic relations over analytic spaces.
\newblock \emph{Math. Struct. Comp. Sci.}, 15:\penalty0 647 -- 670,
  2005{\natexlab{a}}.

\bibitem[Doberkat(2007{\natexlab{a}})]{EED-Book}
E.-E. Doberkat.
\newblock \emph{Stochastic Relations. {F}oundations for {M}arkov Transition
  Systems}.
\newblock Chapman \& Hall/CRC Press, Boca Raton, New York, 2007{\natexlab{a}}.

\bibitem[Doberkat(2008{\natexlab{a}})]{EED-CoAlgLogic}
E.-E. Doberkat.
\newblock Stochastic coalgebraic logic: Bisimilarity and behavioral
  equivalence.
\newblock \emph{Ann. Pure Appl. Logic}, 155:\penalty0 46 -- 68,
  2008{\natexlab{a}}.

\bibitem[Doberkat(2006{\natexlab{b}})]{EED-CongBisim}
E.-E. Doberkat.
\newblock Stochastic relations: congruences, bisimulations and the
  {H}ennessy-{M}ilner theorem.
\newblock \emph{SIAM J. Computing}, 35\penalty0 (3):\penalty0 590~--~626,
  2006{\natexlab{b}}.

\bibitem[Doberkat(2004{\natexlab{a}})]{EED-ConverseProbRel}
E.-E. Doberkat.
\newblock The converse of a probabilistic relation.
\newblock \emph{J. Logic and Algebraic Progr.}, 62\penalty0 (1):\penalty0 133
  -- 154, 2004{\natexlab{a}}.

\bibitem[Doberkat(2004{\natexlab{b}})]{EED-Factoring}
E.-E. Doberkat.
\newblock Factoring stochastic relations.
\newblock \emph{Information Processing Letters}, 90\penalty0 (4):\penalty0
  161~--~166, May 2004{\natexlab{b}}.

\bibitem[Doberkat(2005{\natexlab{b}})]{EED-Hanoi}
E.-E. Doberkat.
\newblock Congruences and bisimulations for continuous-time stochastic logic.
\newblock In Dang~Van Hung and M.~Wirsing, editors, \emph{Proc. ICTAC'2005
  Theoretical Aspects of Computing}, volume 3722 of \emph{Lect. Notes Comp.
  Sci.}, pages 422 -- 436. Springer-Verlag, 2005{\natexlab{b}}.

\bibitem[Doberkat(2007{\natexlab{b}})]{EED-HennessyMilner}
E.-E. Doberkat.
\newblock The {H}ennessy-{M}ilner equivalence for continuous-times stochastic
  logic with mu-operator.
\newblock \emph{J. Appl. Logic}, 35:\penalty0 519 -- 544, 2007{\natexlab{b}}.

\bibitem[Doberkat(2007{\natexlab{c}})]{EED-KleisliMorph}
E.-E. Doberkat.
\newblock Kleisli morphisms and randomized congruences for the {G}iry monad.
\newblock \emph{J. Pure Appl. Alg.}, 211:\penalty0 638--664,
  2007{\natexlab{c}}.

\bibitem[Doberkat(2008{\natexlab{b}})]{EED-Korr-EM-Algebras}
E.-E. Doberkat.
\newblock {E}rratum and {A}ddendum: {E}ilenberg-{M}oore algebras for stochastic
  relations.
\newblock \emph{Information and Computation}, in print, 2008{\natexlab{b}}.

\bibitem[Doberkat(2003)]{EED-SemiPullback}
E.-E. Doberkat.
\newblock Semi-pullbacks and bisimulations in categories of stochastic
  relations.
\newblock In \emph{Proc. ICALP'03}, volume 2719 of \emph{Lect. Notes Comp.
  Sci.}, pages 996~--~1007, Berlin, 2003. Springer-Verlag.

\bibitem[Doberkat and Schubert(2008)]{EED-CS-coalgLogic}
E.-E. Doberkat and C.~Schubert.
\newblock Coalgebraic logic for stochastic right coalgebras.
\newblock \emph{Ann. Pure Appl. Logic (in print)}, 2008.

\bibitem[Dubins and Freedman(1964)]{Dubins+Freedman}
L.~Dubins and D.~Freedman.
\newblock Measurable sets of measures.
\newblock \emph{Pac. J. Math.}, 14:\penalty0 1211 -- 1222, 1964.

\bibitem[Edalat(1999)]{Edalat}
A.~Edalat.
\newblock Semi-pullbacks and bisimulation in categories of {M}arkov processes.
\newblock \emph{Math. Struct. Comp. Science}, 9\penalty0 (5):\penalty0
  523~--~543, 1999.

\bibitem[Edgar(1998)]{Edgar}
G.~A. Edgar.
\newblock \emph{Integral, Probability, and Fractal Measures}.
\newblock Springer-Verlag, New York, 1998.

\bibitem[Engelking(1989)]{Engelking}
R.~Engelking.
\newblock \emph{General Topology}, volume~6 of \emph{Sigma Series in Pure
  Mathematics}.
\newblock Heldermann-Verlag, Berlin, revised and completed edition edition,
  1989.

\bibitem[Fitting(2007)]{Fitting}
M.~Fitting.
\newblock Modal proof theory.
\newblock In P.~Blackburn, J.~van Benthem, and F.~Wolter, editors,
  \emph{Handbook of Modal Logic}, volume~3 of \emph{Studies in Logic and
  Practical Reasoning}, pages 85--138. Elsevier, Amsterdam, 2007.

\bibitem[Fremlin(2000~--~2003)]{Fremlin}
D.~H. Fremlin.
\newblock \emph{Measure Theory}, volume 1~--~4.
\newblock Torres Fremlin, Colchester, 2000~--~2003.

\bibitem[Gamma et~al.(1994)Gamma, Helm, Johnson, and Vlissides]{GangOf4}
E.~Gamma, R.~Helm, R.~Johnson, and J.~Vlissides.
\newblock \emph{Design Patterns --- Elements of Resuable Object-Oriented
  Software}.
\newblock Professional Computing Series. Addison-Wesley, Reading, Mass., 1994.

\bibitem[Giry(1981)]{Giry}
M.~Giry.
\newblock A categorical approach to probability theory.
\newblock In \emph{Categorical Aspects of Topology and Analysis}, number 915 in
  Lect. Notes Math., pages 68~--~85, Berlin, 1981. Springer-Verlag.

\bibitem[Goldblatt(1993)]{Goldblatt-Modality}
R.~Goldblatt.
\newblock \emph{Mathematics of Modality}.
\newblock Number~43 in CSLI Lecture Notes. CSLI Publications, Stanford, 1993.

\bibitem[Goulden and Jackson(1983)]{Goulden+Jackson}
I.~P. Goulden and D.~M. Jackson.
\newblock \emph{Combinatorial Enumeration}.
\newblock Wiley-Interscience Series in Discrete Mathematics. John Wiley \&
  Sons, New York, 1983.

\bibitem[Gr\"atzer(1968)]{Graetzer}
G.~Gr\"atzer.
\newblock \emph{Universal Algebra}.
\newblock The University Series in Higher Mathematics. Van Nostrand, Princeton,
  N.J., 1968.

\bibitem[Halmos(1950)]{Halmos}
P.~R. Halmos.
\newblock \emph{Measure Theory}.
\newblock Van Nostrand Reinhold, New York, 1950.

\bibitem[Hennessy and Milner(1980)]{Hennessy-Milner}
M.~Hennessy and R.~Milner.
\newblock On observing nondeterminism and concurrency.
\newblock In \emph{Proc. ICALP'80}, number~85 in Lect. Notes Comp. Sci., pages
  395~--~409, Berlin, 1980. Springer-Verlag.

\bibitem[Hewitt and Stromberg(1965)]{Hewitt-Stromberg}
E.~Hewitt and K.~R. Stromberg.
\newblock \emph{Real and Abstract Analysis}.
\newblock Springer-Verlag, Berlin, Heidelberg, New York, 1965.

\bibitem[Himmelberg and Vleck(1969)]{Himmelberg-VanVleck-CanJ}
C.~J. Himmelberg and F.~Van Vleck.
\newblock Some selection theorems for measurable functions.
\newblock \emph{Can. J. Math.}, 21:\penalty0 394~--~399, 1969.

\bibitem[Hinderer(1970)]{Hinderer}
K.~Hinderer.
\newblock \emph{Foundations of Non-stationary dynamic programming with discrete
  time parameter}.
\newblock Number~33 in Lect. Notes Op. Re. Math. Syst. Springer-Verlag, Berlin,
  1970.

\bibitem[Jones and Plotkin(1989)]{Jones-Plotkin}
C.~Jones and G.~Plotkin.
\newblock A probabilistic powerdomain of evaluations.
\newblock In \emph{Proc. LICS'89}, pages 186~--~195, IEEE Computer Society
  Press, 1989.

\bibitem[Kechris(1994)]{Kechris}
A.~S. Kechris.
\newblock \emph{Classical Descriptive Set Theory}.
\newblock Graduate Texts in Mathematics. Springer-Verlag, Berlin, Heidelberg,
  New York, 1994.

\bibitem[Keener and Sneyd(2004)]{Keener-Sneyd}
J.~Keener and J.~Sneyd.
\newblock \emph{Mathematical Physiology}.
\newblock Interdisciplinary Applied Mathematics. Springer-Verlag, 2004.

\bibitem[Keimel(2008)]{Keimel-Monads}
K.~Keimel.
\newblock The monad of probability measures over compact ordered spaces and its
  eilenberg-moore algebras.
\newblock Preprint. TU Darmstadt, July 2008.

\bibitem[Knuth(1973)]{Knuth-Art-1}
D.~E. Knuth.
\newblock \emph{The Art of Computer Programming. Vol. I, Fundamental
  Algorithms}.
\newblock Addison-Wesley, Reading, Mass., 2 edition, 1973.

\bibitem[Kupke et~al.(2004)Kupke, Kurz, and Venema]{Kupke-Kurz-Venema}
C.~Kupke, A.~Kurz, and Y.~Venema.
\newblock Stone coalgebras.
\newblock \emph{Theor. Comp. Sci.}, 327\penalty0 (1 - 2):\penalty0 109 -- 134,
  2004.

\bibitem[Kupke et~al.(2008)Kupke, Kurz, and Venema]{Kupke-Kurz-Venema_Moss}
C.~Kupke, A.~Kurz, and Y.~Venema.
\newblock Completeness of the finitary moss logic.
\newblock In C.~Areces and R.~Goldblatt, editors, \emph{Adv. Mod. Logic
  AiML'08}, volume 193~--~218. College Publications, 2008.

\bibitem[Kuratowski(1966)]{Kuratowski}
K.~Kuratowski.
\newblock \emph{Topology}, volume~I.
\newblock PWN - Polish Scientific Publishers and Academic Press, Warsaw and New
  York, 1966.

\bibitem[Kurz(2001)]{Kurz_afterDiss}
A.~Kurz.
\newblock Specifying coalgebras with modal logic.
\newblock \emph{Theor. Comp. Sci.}, 260:\penalty0 119~--~138, 2001.

\bibitem[Lane(1997)]{MacLane}
S.~Mac Lane.
\newblock \emph{Categories for the Working Mathematician}.
\newblock Graduate Texts in Mathematics. Springer-Verlag, Berlin, 1997.

\bibitem[Larsen and Skou(1991)]{Larsen+Skou}
K.~G. Larsen and A.~Skou.
\newblock Bisimulation through probabilistic testing.
\newblock \emph{Information and Computation}, 94:\penalty0 1~--~28, 1991.

\bibitem[Moggi(1991)]{Moggi-Inf+Control}
E.~Moggi.
\newblock Notions of computation and monads.
\newblock \emph{Information and Computation}, 93:\penalty0 55~--~92, 1991.

\bibitem[Moss and Viglizzo(2006)]{Moss-Viglizzo-IuC}
L.~M. Moss and I.~D. Viglizzo.
\newblock Final coalgebras for functors on measurable spaces.
\newblock \emph{Inf. Comput.}, 204:\penalty0 610--636, 2006.

\bibitem[Moss(1999)]{Moss}
L.~S. Moss.
\newblock Coalgebraic logic.
\newblock \emph{Ann. Pure Appl. Logic}, 96:\penalty0 277~--~317, 1999.

\bibitem[Moss and Viglizzo(2004)]{Moss-Viglizzo}
L.~S. Moss and I.~D. Viglizzo.
\newblock Harsanyi type spaces and final coalgebras constructed from satisfied
  theories.
\newblock \emph{ENTCS}, pages 279 -- 295, 2004.

\bibitem[Panangaden(1998)]{Panangaden}
P.~Panangaden.
\newblock Probabilistic relations.
\newblock In C.~Baier, M.~Huth, M.~Kwiatkowska, and M.~Ryan, editors,
  \emph{Proc. PROBMIV}, pages 59~--~74, 1998.

\bibitem[Parthasarathy(1967)]{Parthasarathy}
K.~R. Parthasarathy.
\newblock \emph{Probability Measures on Metric Spaces}.
\newblock Academic Press, New York, 1967.

\bibitem[Pattinson(2004)]{Pattinson}
D.~Pattinson.
\newblock Expressive logics for coalgebras via terminal sequence induction.
\newblock \emph{Notre Dame J. Formal Logic}, 45\penalty0 (1):\penalty0 19 --
  33, 2004.

\bibitem[Pumpl{\"u}n(2003)]{Pumpluen}
D.~Pumpl{\"u}n.
\newblock Positively convex modules and ordered normed linear spaces.
\newblock \emph{J. Convex Analysis}, 10\penalty0 (1):\penalty0 109~--~127,
  2003.

\bibitem[Pumpl\"{u}n(1999)]{Pumpluen-Kategorien}
D.~Pumpl\"{u}n.
\newblock \emph{{E}lemente der {K}ategorientheorie}.
\newblock Spektrum Akademischer Verlag, Heidelberg, 1999.

\bibitem[Rieder(1975)]{Rieder}
U.~Rieder.
\newblock Bayesian dynamic programming.
\newblock \emph{Adv. Appl. Prob.}, 7:\penalty0 330 -- 348, 1975.

\bibitem[Rutten(2000)]{Rutten}
J.~J. M.~M. Rutten.
\newblock Universal coalgebra: a theory of systems.
\newblock \emph{Theor. Comp. Sci.}, 249\penalty0 (1):\penalty0 3~--~80, 2000.
\newblock Special issue on modern algebra and its applications.

\bibitem[Schr{\"o}der(2008)]{Schroeder-Expressivity}
L.~Schr{\"o}der.
\newblock Expressivity of coalgebraic modal logic: the limits and beyond.
\newblock \emph{Theor. Comp. Sci.}, 390:\penalty0 230--247, 2008.

\bibitem[Schr{\"o}der and Pattinson(2007)]{Schroeder-Pattinson}
Lutz Schr{\"o}der and Dirk Pattinson.
\newblock Modular algorithms for heterogeneous modal logics.
\newblock In \emph{Proc. ICALP}, pages 459--471, 2007.

\bibitem[Schubert(2007)]{cs:fossacs08}
Ch. Schubert.
\newblock Coalgebraic modal logic over analytic spaces.
\newblock Technical Report 170, Chair for Software Technology, Technical
  University of Dortmund, Dezember 2007.

\bibitem[Shiryaev(1996)]{Shiryaev}
A.~N. Shiryaev.
\newblock \emph{Probability}, volume~95 of \emph{Graduate Texts in
  Mathematics}.
\newblock Springer-Verlag, Berlin, Heidelberg, New York, second edition, 1996.

\bibitem[Sokolova(2005)]{Sokolova}
A.~Sokolova.
\newblock \emph{Coalgebraic Analysis of Probabilistic Systems}.
\newblock PhD thesis, Department of Computer Science, University of Eindhoven,
  2005.

\bibitem[Srivastava(1998)]{Srivastava}
S.~{M.\ } Srivastava.
\newblock \emph{A Course on Borel Sets}.
\newblock Graduate Texts in Mathematics. Springer-Verlag, Berlin, 1998.

\bibitem[Sun(2000)]{Sun-Economy}
Y.~Sun.
\newblock Economics and nonstandard analysis.
\newblock In P.~A. Loeb and M.~Wolff, editors, \emph{Nonstandard analysis for
  the Working Mathematician}, Mathematics and its Applications, pages 259 --
  305. Kluwer Academic Publishers, Dordrecht, 2000.

\bibitem[v.~Querenburg(2001)]{Querenburg}
B.~v.~Querenburg.
\newblock \emph{{Mengentheoretische Topologie}}.
\newblock Springer -Lehrbuch. Springer-Verlag, Berlin, 3rd edition, 2001.

\bibitem[Viglizzo(2005)]{Viglizzo}
I.~D. Viglizzo.
\newblock Final sequences and final coalgebras for measurable spaces.
\newblock In J.~L. Fiadeiro and J.~Rutten, editors, \emph{Proc. Algebra and
  Coalgebra in Computer Science}, number 3629 in Lect. Notes Comp. Sci., pages
  395~--~407. Springer-Verlag, 2005.

\bibitem[Wagner(1977)]{Wagner}
D.~H. Wagner.
\newblock A survey of measurable selection theorems.
\newblock \emph{SIAM J. Control Optim.}, 15\penalty0 (5):\penalty0 859~--~903,
  August 1977.

\bibitem[Wilf(1990)]{Wilf}
H.~S. Wilf.
\newblock \emph{generatingfunctionology}.
\newblock Academic Press, Boston, 1990.

\bibitem[Wilkinson(2006)]{Wilkinson}
D.~J. Wilkinson.
\newblock \emph{Stochastic Modelling For Systems Biology}.
\newblock Mathematical and Computational Biology Series. Chapman \&
  Hall/CRC-Press, Boca Raton, New York, 2006.

\bibitem[Worrell(2005)]{Worrell-Terminal}
J.~Worrell.
\newblock On the final sequence of a finitary set functor.
\newblock \emph{Theor. Comp. Sci.}, 338\penalty0 (1--3):\penalty0 184--199,
  2005.

\end{thebibliography}
