On the invariant measure for the quasi-linear Lasota equation

The problem of the existence of the invariant measure is important considering its connections with chaotic behaviour. In the papers (Zesz. Nauk. Uniw. Jagiellonskiego, Pr. Mat. 1982; 23:117-123; Ann. Pol. Math. 1983; XLI:129-137; J. Differential Equations 2004; 196:448-465) the existence of invariant and ergodic measures according to the dynamical system generated by the Lasota equation was proved, i.e. the equation describing the dynamics and becoming different of the population of cells. In this paper, the existence of such measure for the quasi-linear Lasota equation is proved. This measure is the carriage of the measure described by Dawidowicz (Zesz. Nauk. Uniw. Jagiellonskiego, Pr. Mat. 1982; 23:117-123).