相关论文: A brief review of Radon-Nikod\'ymification

Some topics concerning the Gould integral are presented here: new results of integrability on finite measure spaces with values in an M-space are given, together with a Radon-Nikodym theorem relative to a Gould-type integral of real…

The Radon transform and its dual are central objects in geometric analysis on Riemannian symmetric spaces of the noncompact type. In this article we study algebraic versions of those transforms on inductive limits of symmetric spaces. In…

This paper presents a new general formulation of the Radon-Nikodym theorem in the setting of abstract measure theory. We introduce the notion of weak localizability for a measure and show that this property is both necessary and sufficient…

Novel analysis of finite dimensional Hilbert space is outlined. The approach bypasses general, inherent, difficulties present in handling angular variables in finite dimensional problems: The finite dimensional, d, Hilbert space operators…

In the theory of inner and outer balayage of positive Radon measures on a locally compact space $X$ to arbitrary $A\subset X$ with respect to suitable, quite general function kernels, developed in a series of the author's recent papers, we…

The aim of this note is to establish two Radon--Nikodym type theorems for nonnegative Hermitian forms defined on a real or complex vector space. We apply these results to prove the known Radon--Nikodym theorems of the theory of…

In this paper we present some results concerning Gould integrability of vector functions with respect to a monotone measure on finitely purely atomic measure spaces. As an application a Radon-Nikodym theorem in this setting is obtained.

We discuss the problem of estimating Radon-Nikodym derivatives. This problem appears in various applications, such as covariate shift adaptation, likelihood-ratio testing, mutual information estimation, and conditional probability…

In this paper, we first introduce $\mathbb{L}$-$\mu$-measurable functions and $\mathbb{L}$-Bochner integrable functions on a finite measure space $(S,\mathcal{F},\mu),$ and give an $\mathbb{L}$-valued analogue of the canonical…

We construct modified energies for the generalized KdV equation. As a consequence, we obtain quasi-invariance of the high order Gaussian measures along with $L^p$ regularity on the corresponding Radon-Nykodim density, as well as new bounds…

We classify the several classes of the set of smooth measures from the perspective of the denseness and the locality, and consider their relationships, in particular, that of the Kato class and Radon measures of finite energy integrals. We…

We analyze some properties of the measures in the dual of the space $BV$, by considering (signed) Radon measures satisfying a perimeter bound condition, which means that the absolute value of the measure of a set is controlled by the…

Under mild conditions, it is possible to obtain, from almost purely measure-theoretic considerations and without any specific reference to stochastic processes, a change-of-measures result, resembling the usual Radon-Nikod\'ym change of…

We study when the integration maps of vector measures can be computed as pointwise limits of their finite rank Radon-Nikod\'ym derivatives. We will show that this can sometimes be done, but there are also principal cases in which this…

In the setting of the Euclidean space equipped with an arbitrary Radon measure, we prove the equivalence between several notions of function of bounded variation present in the literature. We also study the relation between various…

Finite Geometry is used to underpin operators acting in finite, d, dimensional Hilbert space. Quasi distribution and Radon transform underpinned with finite dual affine plane geometry (DAPG) are defined in analogy with the continuous ($d…

For suitable kernels on a locally compact space $X$, we develop a theory of inner balayage of quite general Radon measures $\omega$ (not necessarily of finite energy) to arbitrary $A\subset X$. In the case where $A$ is Borel, this theory…

In this note we give a new proof of a version of the Besicovitch covering theorem, given in \cite{EG1992}, \cite{Bogachev2007} and extended in \cite{Federer1969}, for locally finite Borel measures on finite dimensional complete Riemannian…

We start with a brief overview of the known facts about the spaces of discrete Radon measures those may be considered as generalizations of configuration spaces. Then we study three Markov dynamics on the spaces of discrete Radon measures:…

Let S be a non-exceptional oriented surface of finite type. We classify all Radon measures on the space of measured geodesic laminations for S which are invariant under the mapping class group.