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On Lebesgue nonlinear transformations

Nasir Ganikhodjaev|Ramazon Muhitdinov|M. Saburov
대한수학회 (The Korean Mathematical Society)|2017.03|대한수학회보 (Bulletin of the KMS)|제54권 제2호|pp. 607-618

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참고문헌

키워드

Lebesgue nonlinear transformationquadratic operatormeasurable space
주제분류수학

초록

In this paper, we introduce a quadratic stochastic operators on the set of all probability measures of a measurable space. We study the dynamics of the Lebesgue quadratic stochastic operator on the set of all Lebesgue measures of the set $[0,1]$. Namely, we prove the regularity of the Lebesgue quadratic stochastic operators.

Abstract

In this paper, we introduce a quadratic stochastic operators on the set of all probability measures of a measurable space. We study the dynamics of the Lebesgue quadratic stochastic operator on the set of all Lebesgue measures of the set $[0,1]$. Namely, we prove the regularity of the Lebesgue quadratic stochastic operators.

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