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ON LEBESGUE NONLINEAR TRANSFORMATIONS
Ganikhodjaev, Nasir,Muhitdinov, Ramazon,Saburov, M. Korean Mathematical Society 2017 대한수학회보 Vol.54 No.2
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.
On Lebesgue nonlinear transformations
Nasir Ganikhodjaev,Ramazon Muhitdinov,M. Saburov 대한수학회 2017 대한수학회보 Vol.54 No.2
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.