References
Yu. Al-Kassas, “Metrizability and paracompactness of spaces of probability measures”,Vestn. Mosk. Univ., Ser. Mat. Mekh.,1 (1993).
A. V. Arkhangelskii, “On a class of spaces which contains all metric and all locally bicompact spaces”,Mat. Sb.,67, No. 1, 55–85 (1965).
T. O., Banach, “Soft mappings, trivial bundles and functors in the category of sigma-compact spaces”, in:General Topology. Spaces, Mappings, and Functors, [Russian translation], Moscow Univ. Press, Moscow (1992), pp. 11–22.
T. O. Banach,Topology of Spaces of Probabity Measures, Matem. Studii. Pratsi Lviv, Mathem. Collective,5, 65–87 (1995).
T. O. Banach, “Topology of Spaces of Probability Measures, Matem. studii. Pratsi Lviv, Mathem. Collective,5, 88–106 (1995).
T. O. Banach, “Topological classification of spaces of probability measures on projective spaces”,Mat. Zametki (in press).
T. O. Banach and R. Cauty, “Topological classification of spaces of probability measures of coanalytic sets”,Mat. Zametki,55, No. 1, 10–19 (1994).
T. O. Banach and T. M. Radul, “About a functor of uniform Radon measures”,Dokl. Akad. Nauk Ukr.,8, 16–20 (1994).
T. O. Banach and T. M. Radul, “Topology of spaces of probability measures and geometry of their mappings”,Mat. Sb.,1.
T. O. Banach and T. M. Radul, “Topology of spaces of probability measures and geometry of their mappings,”,Mat. Sb.,2.
N. Bourbaki,Espaces Vectoriels Topologiques, Paris (1955).
N. Bourbaki, “Intégration”, in:Eléménts de Mathématique, Premiére partie: liver VI. Paris (1966).
V. S. Varadarain, “Measures on topological spaces”,Mat. Sb.,55, No. 1, 35–100 (1961).
A. N. Dranishnikov, “OnQ-bundles without disjoint sections”,Funkts. Anal. Prilozhen.,22, No. 2, 79–80 (1988).
B. A. Efimov, “Dyadic bicompacta”,Tr. Mosk. Mat. Ob.,14, 211–247 (1965).
B. A. Efimov, “Mappings and embeddings of dyadic spaces”,Mat. Sb.,103, 211–247 (1977).
T. F. Zhuraev, “The space of all probability measures with finite supports which is homeomorphic to an infinite-dimensional linear space,”, in:General Topology. Spaces and Mappings, Moscow State Univ., Moscow (1989), pp. 66–70.
M. M. Zarichny, “Functors generated by universal mappings of injective limits of sequences of Menger compacta,” in:Mathematics. Research Works [in Russian], Riga. Latvian Univ.,562 (1991), pp. 95–102.
M. M. Zarichny and T. N. Radul, “Monads in the category of compacta”,Usp. Mat. Nauk,50, No. 3, 83–108 (1955).
L. V. Kantorovich, “On the displacement of masses”,Dokl. Akad. Nauk SSSR,37, No. 7/8, 227–229 (1942).
L. V. Kantorovich and G. Sh. Rubinstein, “On a functional space and certain extremal problems”,Dokl. Akad. Nauk SSSR,115, No. 6, 1058–1061 (1957).
L. V. Kantorovich and G. Sh. Rubinstein, “On a space of completely additive functions.Vestn. Leningrad Univ.,7, Issue 2, 52–59 (1958).
R. Cauty, “Property of strong universality and its applications”,Tr. Mosk. Inst. (1996).
A. A. Milyutin, “Isomorphness of spaces of continuous functions over compacta of continual cardinality”,Theory of Functions, Functional Analysis and Applications, Kharkov,2, 150–156 (1966).
A. Pelczynski,Linear Extensions, Linear Averagings and Their Applications to Linear Topological Classification of Spaces of Continuous Functions, Warsaw (1968).
T. N. Radul, “Pairs of spaces of probability measures, which are homeomorphic to (Q, ∑∓),”Theses of the 6th Tiraspol Symposium on General Topology and Applications, Chisinau, 1976–1977 (1991).
T. N. Radul, “On some representations of the pseudointerior of the Hilbert cube in spaces of probability measures”,Vestn. Mosk. Univ., Ser. Mat. Mekh.,3, 79–81 (1993).
T. N. Radul, “On the barycentric mapping of probability measures”,Vestn. Mosk. Univ., Ser. Mat. Mekh.,1, 3–6 (1994).
Yu. V. Sadovnichii, “On a metric on spaces of probability measures”,Vesin. Mosk. Univ., Ser. Mat. Mekh.,4, 31–35 (1994).
Yu. V. Sadovnichii, “On the completion of metric spaces of probability measures”,Vestn. Mosk. Univ., Ser. Mat. Mekh.,5, 28–33 (1994).
Yu. V. Sadovnichii, “On the uniformity on spaces of probability measures”, in:General Topology Mappings, Products, and Dimensionality of Spaces, Mosk. Gos. Univ., Moscow (1994), pp. 119–131.
Yu. V. Sadovnichii, “Uniform spaces of probability measures”,Vestn. Mosk. Univ., Ser. Mat. Mekh.,2, 85–87 (1995).
V. V. Uspenskii, “Free topological groups of metrizable spaces”,Izv. Akad. Nauk SSSR, Ser. Mat.,54, No. 6, 1295–1319 (1990).
V. V. Fedorchuk, “Trivial bundles of spaces of probability measures”,Mat. Sb.,129, No. 4, 473–493 (1986).
V. V. Fedorchuk, “Factorization lemma for open mappings of compacta”,Mat. Zametki,42, No. 1, 101–114 (1987).
V. V. Fedorchuk, “Stratification of spaces of probability measures and geometry of infinite interations of certain monadic functors”,Dokl. Akad. Nauk SSSR,307, No. 1, 41–45 (1988).
V. V. Fedorchuk, “Triples of infinite iterations of metrizable functors”,Izv. Akad. Nauk SSSR, Ser. Mat.,54, No. 2, 394–418 (1990).
V. V. Fedorchuk, “On the softness of mappings of subsets of locally convex spaces”,Usp. Mat. Nauk,45, No. 2, 221–222 (1990).
V. V. Fedorchuk, “Probability measures in topology”,Usp. Mat. Nauk,46, No. 1, 41–80 (1991).
V. V. Fedorchuk, “On the mapping of a barycenter of probability measures”, Vestn. Mosk. Univ., Ser. Mat. Mekh.,1, 42–47 (1992).
V. V. Fedorchuk, “On barycentrically open bicompacta,”Sib. Mat. Zh.,33, No. 4, 205–210 (1992).
V. V. Fedorchuk and V. V. Filippov,General Topology. Main Constructions [in Russian], Moscow Univ. Press, Moscow (1988).
A. Ch. Chigogidze, “On the extension of normal functors”,Vestn. Mosk. Univ., Ser. Mat. Mekh.,6, 23–26 (1984).
E. V. Schepin, “On Tychonoff manifolds”,Dokl. Akad. Nauk SSSR,246, 551–554 (1979).
E. V. Shchepin, “Functors and uncountable degree of compacta”,Usp. Mat. Nauk,36, No. 3, 3–62 (1981).
R. R. Engelking,Genral Topology, PWN, Warszawa (1983).
T. Banach, “AE(O)-spaces and regular operators extending averaging pseudometrics”,Bull. Pol. Acad. Sci. Math.,42, No. 3, 197–206 (1994).
T. Banach, T. Dobrowolski, and A. Plichko,Topology of Operator Images, Preprint.
T. Banach and T. Radul, “On barycentrically soft compacta and affine retracts of products of metrizable convex compacta,”Matematichni Studii. Pratsi Lviv Mat. Soc. (1996).
T. Banach and K. Sakai,Characterization of (ℝ∞, σ)- or (Q ∞, ∑)-Manifolds, Preprint.
Cz. Bessaga and A. Pelczinski,Selected Topics in Infite-Dimensional Topology, PWN, Warszawa (1975).
M. Bestvina and J. Mogilski, “Characterizing certain incomplete infinite-dimensional absolute retracts,”Michigan Math. J.,33, 291–313 (1986).
R. Cauty, “Ensembles absorbants pour les classes projectives”,Fund. Math.,143, 203–206 (1993).
J. G. Ceder, “Some generalizations of metric spaces”,Pacif. J. Math.,2, 105–126 (1961).
S. Ditor and L. Eifler, “Some open mappings theorems for measures”,Trans. AMS,164, 163–172 (1972).
S. Ditor and R. Haydon, “On absolute retracts,P(S) and complemented subspaces ofC(D ω1),Studia Math.,56, No. 3, 243–251 (1976).
T. Dobrowolski and K. Sakai,Spaces of Measures of Metrizable Spaces, Preprint.
S. Eilenberg and T. Moore, “Adjoint functors and triples. III,”J. Math.,9, No. 3, 381–398 (1965).
V. V. Fedorchuk, “The Suslin number of the functor of probability measures,”Topol. Appl. (in print).
V. V. Fedorchuk and Yu. Al-Kassas, “On cellularity of spaces of probability measures with finite supports,”J. Egypt. Math. Soc.,3, 41–47 (1995).
V. V. Fedorchuk and S. Todorĉević, “Cellularity of covarant functors,”Topol. Appl. (in print).
R. J. Gardner and W. F. Pfeffer,Borel Measures. Handbook of Set-Theoretic Topology, North Holland, Amsterdam, 961–1043 (1984).
J. Gerlits, “On subspaces of dyadic compacta,”Studia Sci. Math. Hungar.,11, 115–120 (1976).
B.-L. Guo and K. Sakai, “Spaces of measures on stratifiable spaces,”Kobe J. Math. (in print).
V. G. Gutev,Trivial Bundles of Spaces of Probability Measures and Countable-Dimensionality, Preprint.
J. Hagler, “On the structure ofS andC(S) forS dyadic,”Trans. AMS,214, 415–428 (1975).
R. Haydon, “On a problem of Pelczynski: Milutin spaces, Dungudji spaces andAE(0-dim),”Studia Math.,52, 23–31 (1974).
R. Haydon, “EmbeddingD τ in Dugundji spaces with an application to linear topological classification of spaces of continuous functions”,Studia Math.,56, No. 3, 229–242 (1976).
A. S. Kechris,Classical Descriptive Set Theory, Springer-Verlag, Berlin (1995).
V. L. Klee, “Some topological properties of convex sets,”Trans. AMS,78, 30–45 (1955).
E. Michael, “Continuous selections. I,”Ann. Math.,63, 361–382 (1956).
E. Michael, “Continuous selections. II,”Ann. Math.,64, No. 2, 562–580 (1956).
Nguyen To Nhu and K. Sakai,Probability Measure Functors Preserving Infinite-Dimensional Spaces, Preprint.
T. Radul, “Borelian subsets in the space of probability measures,”Proc. 9th Intern. Conf. on Topol. and Appl., Kiev (1992), p. 115.
T. Radul, “On barycentrically soft compacta,”Fund. Math.,148, 27–33 (1995).
M. M. Zarichnyi, “On universal maps and spaces of probability measures with finite supports,”Matematichni studii Pratsi Lviv mat. tov., No. 2, 78–82 (1993).
Additional references
L. B. Shapiro, “On operators of function extensions and normal functors,”Vestn. Mosk. Univ., Ser. Math. Mekh.,1, 35–42 (1992).
L. B. Shapiro, “On the homogeneity of dyadic bicompacta,”Mat. Zametki,54, No. 4, 117–139 (1993).
J. C. Oxtoby and V. S. Prasad, “Homeomorphic measures in the Hilbert cube,”Pacif. J. Math.,77, No. 2, 483–497 (1978).
Additional information
The review is devoted to the functors of probability measures acting in the categories of compact, Tychonoff, metric, and uniform spaces.
Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Ozory, Vol. 36, Functional Analysis-1, 1996.
Rights and permissions
About this article
Cite this article
Fedorchuk, V.V. Functors of probability measures in topological categories. J Math Sci 91, 3157–3204 (1998). https://doi.org/10.1007/BF02432852
Issue Date:
DOI: https://doi.org/10.1007/BF02432852