On the existence of invariant measures for piecewise monotonic transformations

Lasota, A.; Yorke, James A.

doi:10.1090/S0002-9947-1973-0335758-1

On the existence of invariant measures for piecewise monotonic transformations
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by A. Lasota and James A. Yorke PDF

Trans. Amer. Math. Soc. 186 (1973), 481-488 Request permission

Abstract:

A class of piecewise continuous, piecewise ${C^1}$ transformations on the interval [0, 1] is shown to have absolutely continuous invariant measures.

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