Product of Measurable Spaces and Applications

Roman Frič

doi:10.2478/tmmp-2019-0018

.blurhash-client-img { display: none !important; }

Product of Measurable Spaces and Applications

Tatra Mountains Mathematical Publications

Volume 74 (2019): Issue 1 (December 2019)

By: Roman Frič

Open Access

|Nov 2019

Abstract

We deal with products of measurable spaces and relationships between measures on products and asymmetrical stochastic dependence/independence of one extended probability space on another one.

References

[1] ADÁMEK, J.: Theory of Mathematical Structures. Reidel, Dordrecht, 1983.
Search in Google Scholar Back to article
[2] BABICOVÁ, D.: Probability integral as a linearization, Tatra Mt. Math. Publ. 72 (2018), 1–15.10.2478/tmmp-2018-0017
Search in Google Scholar Back to article
[3] BABICOVÁ, D.—FRIČ, R.: Real functions in stochastic dependence. Tatra Mt. Math. Publ. 74 (2019), 47–56.10.2478/tmmp-2019-0018
Search in Google Scholar Back to article
[4] DVUREČENSKIJ, A.—PULMANNOVÁ, S.: New Trends in Quantum Structures.Kluwer Academic Publ. and Ister Science, Dordrecht and Bratislava, 2000.10.1007/978-94-017-2422-7
Search in Google Scholar Back to article
[5] ELIAŠ, P.—FRIČ, R.: Factorization of observables, Internat. J. Theoret. Phys. 56 (2017), 4073–4083.10.1007/s10773-017-3436-1
Search in Google Scholar Back to article
[6] FRIČ, R.: Remarks on statistical maps and fuzzy (operational) random variables,Tatra Mt. Math. Publ. 30 (2005), 21–34.
Search in Google Scholar Back to article
[7] FRIČ, R.—PAPČO, M.: A categorical approach to probability, Studia Logica 94 (2010), 215–230.10.1007/s11225-010-9232-z
Search in Google Scholar Back to article
[8] _______ Fuzzification of crisp domains,Kybernetika 46 (2010), 1009–1024.
Search in Google Scholar Back to article
[9] _______ On probability domains, Internat. J. Theoret. Phys. 49 (2010), 3092–3100.10.1007/s10773-009-0162-3
Search in Google Scholar Back to article
[10] _______ On probability domains II, Internat. J. Theoret. Phys. 50 (2011), 3778–3786.10.1007/s10773-011-0855-2
Search in Google Scholar Back to article
[11] _______ On probability domains III, Internat. J. Theoret. Phys. 54 (2015), 4237–4246.10.1007/s10773-014-2471-4
Search in Google Scholar Back to article
[12] _______ Upgrading probability via fractions of events, Commun. Math. 24 (2016), 29–41.10.1515/cm-2016-0004
Search in Google Scholar Back to article
[13] _______ On probability domains IV, Internat. J. Theoret. Phys. 56 (2017), 4084–4091.10.1007/s10773-017-3438-z
Search in Google Scholar Back to article
[14] _______ Probability from classical to fuzzy, Fuzzy Sets Syst. 326 (2017), 106–114.10.1016/j.fss.2017.06.003
Search in Google Scholar Back to article
[15] GUDDER, S.: Fuzzy probability theory, Demonstratio Math. 31 (1998), 235–254.10.1515/dema-1998-0128
Search in Google Scholar Back to article
[16] KOLMOGOROV, A. N.: Grundbegriffe der Wahrscheinlichkeitsrechnung. Springer-Verlag, Berlin, 1933.10.1007/978-3-642-49888-6
Search in Google Scholar Back to article
[17] LOÈVE, M.: Probability Theory. D. Van Nostrand Inc., Princeton, New Jersey, 1963.
Search in Google Scholar Back to article
[18] MESIAR, R.: Fuzzy sets and probability theory, Tatra Mt. Math. Publ. 1 (1992), 105–123.
Search in Google Scholar Back to article
[19] NAVARA, M.: Probability theory of fuzzy events. In: Fourth Conference of the European Society for Fuzzy Logic and Technology and 11 Rencontres Francophones sur la Logique Floue et ses Applications (E. Montseny, P. Sobrevilla, eds.), Universitat Politecnica de Catalunya, Barcelona, Spain, 2005, pp. 325–329.
Search in Google Scholar Back to article
[20] PAPČO, M.: On measurable spaces and measurable maps, Tatra Mt. Math. Publ. 28 (2004), 125–140.
Search in Google Scholar Back to article
[21] _______ On fuzzy random variables: examples and generalizations, Tatra Mt. Math. Publ. 30 (2005), 175–185.
Search in Google Scholar Back to article
[22] _______ On effect algebras, Soft Comput. 12 (2008), 373–379.10.1007/s00500-007-0171-1
Search in Google Scholar Back to article
[23] _______ Fuzzification of probabilistic objects. In: 8th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT 2013) (2013), pp. 67–71.
Search in Google Scholar Back to article
[24] RIEČAN, B.—NEUBRUNN, T.: Integral, Measure and Ordering. Kluwer Acad. Publ., Dordrecht-Boston-London, 1997.10.1007/978-94-015-8919-2
Search in Google Scholar Back to article
[25] RIEČAN, B.—MUNDICI, D.: Probability on MV-algebras. In: Handbook of Measure Theory, Vol. II (E. Pap, ed.), North-Holland, Amsterdam, 2002, pp. 869–910.10.1016/B978-044450263-6/50022-1
Search in Google Scholar Back to article
[26] ZADEH, L. A.: Probability measures of fuzzy events, J. Math. Anal. Appl. 23 (1968), 421–427.10.1016/0022-247X(68)90078-4
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2019-0018 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

Journal RSS Feed

Language: English

Page range: 47 - 56

Submitted on: May 23, 2019

Published on: Nov 15, 2019

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

Measurable space,

measurable function,

product of measurable spaces,

probability measure on product,

probability integral,

observable,

degenerated observable,

statistical map,

joint probability space,

extended probability space,

g-joint extended probability space,

stochastic dependence,

asymmetrical stochastic independence,

extended outcome,

conditional expectation,

conditional probability

Related subjects:

Mathematics,

General mathematics

© 2019 Roman Frič, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 74 (2019): Issue 1 (December 2019)