On Some Properties of Measurable Functions in Abstract Spaces

Evgenii Borisenko; Oleg Zubelevich

doi:10.68381/jca29042

Abstract

We present several infinite dimensional theorems which generalize corresponding facts from the finite dimensional differential inclusions theory.

Author information

Contact details are reproduced from the original publication and may be historical.

Evgenii Borisenko

Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia
and: Mechanics and Mathematics Faculty, Lomonosov State University, Moscow, Russia

yevhenii16@yandex.ru

Oleg Zubelevich

Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia
and: Mechanics and Mathematics Faculty, Lomonosov State University, Moscow, Russia

ozubel@yandex.ru

Keywords

Differential inclusions
Filippov's solutions
nonsmooth ODEs

Mathematics Subject Classification

34A60, 49J52, 46G12, 46G10, 28C20

References

P. S. Aleksandrov: Introduction to Set Theory and General Topology (Russian), Nauka, Moscow (1986).Google Scholar
A. F. Filippov: Differential equations with discontinuous right-hand sides, Trans. Am. Math. Soc. 42 (1964) 199–231.https://doi.org/10.1090/trans2/042/13 Google Scholar
K. Kuratowski, J. Jaworowski: Topology. Volume 1, Academic Press, New York (1966).https://doi.org/10.1016/B978-0-12-429201-7.50005-3 Google Scholar
A. P. Robertson, W. J. Robertson: Topological Vector Spaces, Cambridge Tracts in Mathematics and Mathematical Physics 53, Cambridge University Press, Cambridge (1964).Google Scholar
W. Rudin: Real and Complex Analysis, 2nd ed., McGraw-Hill, New York (1974).Google Scholar

Suggested citation

Published by Heldermann Verlag, 2022. Rights now held by Banach Press LLC.

[1] P. S. Aleksandrov: Introduction to Set Theory and General Topology (Russian), Nauka, Moscow (1986).Google Scholar

[2] A. F. Filippov: Differential equations with discontinuous right-hand sides, Trans. Am. Math. Soc. 42 (1964) 199–231.https://doi.org/10.1090/trans2/042/13 Google Scholar

[3] K. Kuratowski, J. Jaworowski: Topology. Volume 1, Academic Press, New York (1966).https://doi.org/10.1016/B978-0-12-429201-7.50005-3 Google Scholar

[4] A. P. Robertson, W. J. Robertson: Topological Vector Spaces, Cambridge Tracts in Mathematics and Mathematical Physics 53, Cambridge University Press, Cambridge (1964).Google Scholar

[5] W. Rudin: Real and Complex Analysis, 2nd ed., McGraw-Hill, New York (1974).Google Scholar