WHEN IS THE FUNCTIONS MEASURABLE?

Authors

  • Ro’zimova Sarvinoz Jumanazar qizi

Keywords:

Keywords: measurable functions, composition, Lebesgue measure

Abstract

In this article we explore under which conditions on the interior function the
composition of functions is measurable. We also study the sharpness of the result by
providing a counterexample for weaker hypotheses.

References

References

de Amo, E., Diaz Carrillo, M., Fernandez-Sanchez, J.: Functionc with Unusual

Differentiability Properties. Annals of the Alexandru Ioan Cuza University –

Mathematics (2014)

cabada, A., Pouso, R.L.: Extremal solutions of strongly nonlinear discontinuous

second-order equations with nonlinear functional boundary conditions. Nonlinear

Analysis 42(8)., 1377-1396 (2000)

Folland, G>B.: Real analysis: modern techniques and their applications, 2 edn.

PAM. Wiley (1999)

Monteiro, G.A., Slavik, A., Tvrdy, M.: Kurzweil- Stieltjes Integral: theory and

applications. World Scientific, Singapore (2018)

Marquez Albes, I., Tojo, F.A.F.: Existence and Uniqueness of Solution for Stieltjes

Differential Equations with Several Derivators. Mediterranean Journal of

Mathematics 18(5), 181(2021)

Munroe, M.E.: Introduction to measure and integration. Addison-Wesley

Cambridge, Mass. (1953)

Natanson, I.: Theory of functions of a real variable, Vol.I, rev.ed. 5 pr. Edn. Ungar

(1983)

Saks, S.: Theory of the Integral, 2 edn. Dover Books on Advanced Mathematics.

Dover, New York (1964)

Spataru, S.: An absolutely continuous function whose inverse function is not

absolutely continuous. Note di Matematica 1 (2004).

Published

2024-08-02

How to Cite

Ro’zimova Sarvinoz Jumanazar qizi. (2024). WHEN IS THE FUNCTIONS MEASURABLE? . TADQIQOTLAR.UZ, 43(1), 47–51. Retrieved from https://tadqiqotlar.uz/new/article/view/4142