Proceedings of the American Mathematical Society

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Some dual statements concerning Wiener measure and Baire category


Author: K. Simon
Journal: Proc. Amer. Math. Soc. 106 (1989), 455-463
MSC: Primary 26A18; Secondary 26A27, 28C20
MathSciNet review: 961409
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Abstract: This paper deals with the duality between Wiener measure and Baire category on $ C_0^1$, the set of continuous functions $ f:[0,1] \to [0,1]$ endowed with the supremum norm. We prove that some properties shared by a residual set of continuous functions, e.g. the typical level set structure, and the existence of periodic points of order 3 hold a.e. with respect to the Wiener measure.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0961409-6
Article copyright: © Copyright 1989 American Mathematical Society