The prevalent dimension of graphs (Q5918076)

A way to extend measure theoretic ``almost everywhere'' to an infinite dimensional space is based on the notion of prevalence. In the article the upper entropy dimension \(\widehat {\triangle }\) is used to obtain the Theorem: Denote for \(f\in C[0,1]\) the graph \(G(f)=\{(x,f(x)): x\in [0,1]\}\). Then the set \(\{f\in C[0,1]: \widehat {\triangle }(G(f))=2\}\) is a prevalent subset of \(C[0,1]\).