On the Lebesgue nonlinear transformations
  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 
Nasir Ganikhodjaev, Mansoor Saburov, Ramazon Muhitdinov
math.DS