On lebesque nonlinear transformation with family of continuos measures - Ganikhodjaev, Nasir; Jusoo, Siti Hasana (American Institute of Physics ( AIP publishing ), 2016)
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 Lebesque quadratic stochastic operator on the set of all Lebesque measures of the set [0,1] and prove the regularity of the Lebesque quadratic stochastic operators.