Abstract
This paper deals with the duality between Wiener measure and Baire category on C 0 1 C_0^1 , the set of continuous functions f : [ 0 , 1 ] → [ 0 , 1 ] 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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