Absolute continuity of analytic 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

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...

On the Continuity and Absolute Continuity of Credibility Functions ∗

The objective of this paper is to study some new analytical properties of credibility functions. We first discuss the continuity of credibility functions, and establish the sufficient and necessary conditions for the right continuity and left continuity of credibility functions. Furthermore, we study the absolute continuity of credibility functions and obtain some sufficient conditions for the ...

Pointwise Differentiability and Absolute Continuity

This paper is concerned with the relationships between L differentiability and Sobolev functions. It is shown that if / is a Sobolev function with weak derivatives up to order k in L , and 0 s / s k, then / has an L derivative of order / everywhere except for a set which is small in the sense of an appropriate capacity. It is also shown that if a function has an 2V derivative P everywhere excep...