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 On Lebesgue nonlinear transformations Bull. Korean Math. Soc. 2017 Vol. 54, No. 2, 607-618 https://doi.org/10.4134/BKMS.b160212Published online March 31, 2017 Nasir Ganikhodjaev, Ramazon Muhitdinov, and M. Saburov P.O. Box 25200, Kuantan, Bukhara State University, P.O. Box 25200, Kuantan 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. Keywords : Lebesgue nonlinear transformation, quadratic operator, measurable space MSC numbers : 47HXX, 46TXX Downloads: Full-text PDF