Some prevalent results about strongly monoHolder functions

We study the typical behaviour of strongly monoHolder functions from the prevalence point of view. To this end we first prove wavelet-based criteria for strongly monoHolder functions. We then use the notion of prevalence to show that the functions of C-alpha(R-d) are almost surely strongly monoHolder with Holder exponent a. Finally, we prove that for any alpha is an element of (0, 1) on a prevalent set of C-alpha(R-d) the Hausdorff dimension of the graph is equal to d + 1 - alpha.