Some Dual Statements Concerning Wiener Measure and Baire Category

K. Simon
1989 Proceedings of the American Mathematical Society  
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