Wavelets and multiresolution analysis: Nature of epsilon((infinity)) Cantorian space-time

In this paper, starting from El Naschic E-infinity Cantorian space-time, we consider the link between the Brownian motion presented by the first author in some earlier papers in the context of cosmology and the multiresolution analysis based on the wavelet transform. We will consider the hypothesis that the present hierarchical segregated Universe is the effect of an expansion, which follows a scaling law. We will give a mathematical method to support El Naschie's picture of the resolution dependence of the observations. In other words, this confirms the vision in which everything we see or measure is resolution dependent.