Abstract
Some related questions concerning the measurability properties of real-valued functions with respect to a certain class of measures are discussed.
Dedicated to Professor Vakhtang Kokilashvili on the occasion of his 80th birthday
Funding source: Shota Rustaveli National Science Foundation
Award Identifier / Grant number: FR/116/5-100/14
Funding statement: The research was partially supported by Shota Rustaveli National Science Foundation, Grant no. FR/116/5-100/14.
References
[1] M. Beriashvili and A. Kirtadze, Non-separable extensions of invariant Borel measures and measurability properties of real-valued functions, Proc. A. Razmadze Math. Inst. 162 (2013), 111–115. 10.1515/gmj-2014-0010Search in Google Scholar
[2] M. Beriashvili and A. Kirtadze, On the uniqueness property of non-separable extensions of invariant Borel measures and relative measurability of real-valued functions, Georgian Math. J. 21 (2014), no. 1, 49–56. 10.1515/gmj-2014-0010Search in Google Scholar
[3] E. Bernstein, Zur Theorie der trigonometrischen Reihen, Sitzungsber. Sachs. Akad. Wiss. Leipzig. Math. Natur. Kl. 60 (1908), 325–338. Search in Google Scholar
[4] T. Gill, A. Kirtadze, G. Pantsulaia and A. Plichko, Existence and uniqueness of translation invariant measures in separable Banach spaces, Funct. Approx. Comment. Math. 50 (2014), no. 2, 401–419. 10.7169/facm/2014.50.2.12Search in Google Scholar
[5] T. Gill, A. Kirtadze, G. Pantsulaia, A. Plichko and N. Rusiashvili, On ordinary and standard “Lebesgue measures” in separable Banach spaces, Georgian Int. J. Sci. Technol. Med. 5 (2013), no. 3–4, 115–134. Search in Google Scholar
[6] T. L. Gill and W. W. Zachary, Functional Analysis and the Feyman Operator Calculus, Springer, Cham, 2016. 10.1007/978-3-319-27595-6Search in Google Scholar
[7] A. B. Kharazishvili, Elements of Combinatorical Theory of Infinite Sets (in Russian), Tbilisi Gos. University, Tbilisi, 1981. Search in Google Scholar
[8] A. B. Kharazishvili, Topics in Measure Theory and Real Analysis, Atlantis Stud. Math. 2, Atlantis Press, Paris, 2009. 10.2991/978-94-91216-36-7Search in Google Scholar
[9] A. B. Kharazishvili, Set Theoretical Aspects of Real Analysis, Monogr. Res. Notes Math., CRC Press, Boca Raton, 2015. 10.1201/b17298Search in Google Scholar
[10] A. Kharazishvili and A. Kirtadze, On the measurability of functions with respect to certain classes of measures, Georgian Math. J. 11 (2004), no. 3, 489–494. 10.1515/GMJ.2004.489Search in Google Scholar
[11] K. Kuratowski, Topology. Vol. I, Academic Press, New York, 1966. Search in Google Scholar
[12] J. C. Morgan, II, Point Set Theory, Monogr. Textb. Pure Appl. Math. 131, Marcel Dekker, New York, 1990. Search in Google Scholar
[13] J. C. Oxtoby, Measure and Category. A Survey of the Analogies Between Topological and Measure Spaces, Grad. Texts in Math. 2, Springer, New York, 1971. 10.1007/978-1-4615-9964-7Search in Google Scholar
© 2018 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Approximation in generalized Morrey spaces
- On the Cauchy problem for a generalized nonlinear heat equation
- A new principle for arbitrary meromorphic functions in a given domain
- On some generalized Painlevé and Hayman type equations with meromorphic solutions in a bounded domain
- On measurability of real-valued functions in infinite-dimensional topological vector spaces
- A modular variable Orlicz inequality for the local maximal operator
- On the Rellich inequality in Lp(·)(a,b)
- On a generalization of Smirnov’s theorem with some applications
- Space quasiconformal mappings and Neumann eigenvalues in fractal type domains
- Necessary and sufficient condition for the boundedness of the Gegenbauer–Riesz potential on Morrey spaces
- Summability on non-rectifiable Jordan curves
- On generalized fractional cosine and sine transforms
- On mixed norm Bergman–Orlicz–Morrey spaces
- Sharp estimates for the gradient of the generalized Poisson integral for a half-space
- Grand Lebesgue sequence spaces
- Generalized fractional integral operators on generalized Orlicz–Morrey spaces of the second kind over non-doubling metric measure spaces
- A note on N. Bary’s one conjecture
Articles in the same Issue
- Frontmatter
- Approximation in generalized Morrey spaces
- On the Cauchy problem for a generalized nonlinear heat equation
- A new principle for arbitrary meromorphic functions in a given domain
- On some generalized Painlevé and Hayman type equations with meromorphic solutions in a bounded domain
- On measurability of real-valued functions in infinite-dimensional topological vector spaces
- A modular variable Orlicz inequality for the local maximal operator
- On the Rellich inequality in Lp(·)(a,b)
- On a generalization of Smirnov’s theorem with some applications
- Space quasiconformal mappings and Neumann eigenvalues in fractal type domains
- Necessary and sufficient condition for the boundedness of the Gegenbauer–Riesz potential on Morrey spaces
- Summability on non-rectifiable Jordan curves
- On generalized fractional cosine and sine transforms
- On mixed norm Bergman–Orlicz–Morrey spaces
- Sharp estimates for the gradient of the generalized Poisson integral for a half-space
- Grand Lebesgue sequence spaces
- Generalized fractional integral operators on generalized Orlicz–Morrey spaces of the second kind over non-doubling metric measure spaces
- A note on N. Bary’s one conjecture