A refined form of Lebesgue's decomposition theorem decomposes a singular measure into a singular continuous measure and a discrete measure. See below for ...

18 авг. 2012 г. · μ and ν are said to be singular (or also mutually singular, or orthogonal) if there are two sets A,B∈B such that A∩B=∅, A∪B=X and μ(B)=ν(A)=0.

14 янв. 2012 г. · A singular (say, probability) measures μ with respect to the Lebesgue measure λ on Rd satisfies by definition: there exists a Borel set S such ... Properties of mutual singular measures - Math Stack Exchange definition of singular measure - radon nikodym The Cantor distribution is singular (with respect to lebesgue ... Другие результаты с сайта math.stackexchange.com

A discrete singular measure (with respect to Lebesgue measure on the reals) is a measure supported at 0, say iff . In general, a measure is concentrated on a ...

4 янв. 2009 г. · In this section we investigate the structure of this space, together with the closely related spaces of signed measures and finite measures.

We show that µ is singular with respect to Lebesgue measure if and only if the set of those c for which µ and τcµ are mutually singular is dense (Theorem 1).

22 окт. 2024 г. · Another characterization of singularity (Theorem \ref{thm:9}.) is the existence of a set of full μ \mu measure that has continuum many disjoint ...

5 февр. 2013 г. · Abstract:In this paper, we are interested in the spectral properties of the generalised principal eigenvalue of some nonlocal operator.

Abstract: A natural definition is introduced for the Hilbert transform on an L2-space with respect to a singular measure on the real line. It is defined as ...