Absolute continuity of non-homogeneous self-similar measures

Self-Similar Measures

On the Absolute Continuity of a Class of Invariant Measures

Let X be a compact connected subset of Rd, let Sj , j = 1, ...,N , be contractive self-conformal maps on a neighborhood of X, and let {pj(x)}j=1 be a family of positive continuous functions on X. We consider the probability measure μ that satisfies the eigen-equation

Absolute Continuity and Singularity of Probability Measures in Functional Spaces

Self-Similar Measures for Quasicrystals

We study self-similar measures of Hutchinson type, defined by compact families of contractions, both in a single and multi-component setting. The results are applied in the context of general model sets to infer, via a generalized version of Weyl’s Theorem on uniform distribution, the existence of invariant measures for families of self-similarities of regular model sets.

Absolute Continuity between the Wiener and Stationary Gaussian Measures

It is known that the entropy distance between two Gaussian measures is finite if, and only if, they are absolutely continuous with respect to one another. Shepp [5] characterized the correlations corresponding to stationary Gaussian measures that are absolutely continuous with respect to the Wiener measure. By analyzing the entropy distance, we show that one of his conditions, involving the spe...