# ON LEBESGUE NONLINEAR TRANSFORMATIONS

• Ganikhodjaev, Nasir (Department of Computational & Theoretical Sciences Faculty of Science International Islamic University Malaysia) ;
• Muhitdinov, Ramazon (Bukhara State University) ;
• Saburov, M. (Department of Computational & Theoretical Sciences Faculty of Science International Islamic University Malaysia)
• Published : 2017.03.31

#### 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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