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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Approximating the absolutely continuous measures invariant under general maps of the interval


Author: Abraham Boyarsky
Journal: Proc. Amer. Math. Soc. 87 (1983), 475-480
MSC: Primary 28D05; Secondary 41A30, 58F11, 58F20
DOI: https://doi.org/10.1090/S0002-9939-1983-0684642-4
MathSciNet review: 684642
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Abstract: Let $ \tau :I \to I$ be a nonsingular, piecewise continuous transformation which admits a unique absolutely continuous invariant measure $ \mu $ with density function $ {f^ * }$. The main result establishes the fact that $ {f^ * }$ can be approximated weakly by the density functions of a sequence of measures invariant under piecewise linear Markov maps $ \left\{ {{\tau _n}} \right\}$ which approach $ \tau $ uniformly.


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DOI: https://doi.org/10.1090/S0002-9939-1983-0684642-4
Article copyright: © Copyright 1983 American Mathematical Society