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Proceedings of the American Mathematical Society

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

 

 

Nonincrease almost everywhere of certain measurable functions with applications to stochastic processes


Author: Simeon M. Berman
Journal: Proc. Amer. Math. Soc. 88 (1983), 141-144
MSC: Primary 60G17; Secondary 60J55
MathSciNet review: 691295
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Abstract: Let $ x(t)$, $ 0 \leqslant t \leqslant 1$, be a real valued measurable function having a local time $ {\alpha _{[0,t]}}(x)$, $ 0 \leqslant t \leqslant 1$. If the latter is continuous in $ t$ for almost all $ x$, then almost every $ t$ is not a point of increase of the function $ x( \cdot )$.


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DOI: https://doi.org/10.1090/S0002-9939-1983-0691295-8
Keywords: Local time, point of increase
Article copyright: © Copyright 1983 American Mathematical Society