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This paper deals with the duality between Wiener measure and Baire category on C¿ , the set of continuous functions /: [0,1] -» [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.doi:10.2307/2048827 fatcat:pbnw5w7chndtjktwgirasr6kia