In this paper we discuss how to construct piecewise linear chaotic maps with a prescribed probability distribution on a finite number of open intervals of equal length that form a partition of the unit interval. The idea and method of how to find such a map are given in . But a formal proof is not given. In this paper we provide a formal proof.
"On Constructing Chaotic Maps with a Prescribed Probability Distribution." Missouri J. Math. Sci. 30 (1) 77 - 84, May 2018. https://doi.org/10.35834/mjms/1534384957