Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete

, Volume 69, Issue 3, pp 461-478

First online:

Generalized bounded variation and applications to piecewise monotonic transformations

  • Gerhard KellerAffiliated withInstitut für Angewandte Mathematik, Universität Heidelberg

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We prove the quasi-compactness of the Perron-Frobenius operator of piecewise monotonic transformations when the inverse of the derivative is Hölder-continuous or, more generally, of bounded p-variation.