Related papers: Topics of Measure Theory on Infinite Dimensional S…
A space for gauge theories is defined, using projective limits as subsets of Cartesian products of homomorphisms from a lattice on the structure group. In this space, non-interacting and interacting measures are defined as well as functions…
A number of topics involving metrics and measures are discussed, including some of the special structure associated with ultrametrics.
We study certain infinite-dimensional probability measures in connection with frame analysis. Earlier work on frame-measures has so far focused on the case of finite-dimensional frames. We point out that there are good reasons for a sharp…
A construction of product measures is given for an arbitrary sequence of measure spaces via outer measure techniques without imposing any condition on the underlying measure spaces. This approach concludes finally the problem of the…
Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…
We construct surface measures associated to Gaussian measures in separable Banach spaces, and we prove several properties including an integration by parts formula.
A construction of product measures is given for an arbitrary sequence of measure spaces via outer measure techniques without imposing any condition on the underlying measure spaces. This result generalises the ones given up to date.
This is an introduction to measure theory, integration and function spaces, with all the needed preliminaries included, and with some applications included as well. We first discuss some basic motivations, coming from discrete probability,…
These lecture notes contain an introduction to some of the fundamental ideas and results in analysis and probability on infinite-dimensional spaces, mainly Gaussian measures on Banach spaces. They originated as the notes for a topics course…
The primary objective of the present paper is to develop the theory of quantization dimension of an invariant measure associated with an iterated function system consisting of finite number of contractive infinitesimal similitudes in a…
One of the goals of this article is to define a an unified setting adapted to the description of means (normalized integrals or invariant means) on an infinite product of measured spaces with infinite measure. We first remark that some…
In this short note we present several infinite dimensional theorems which generalize corresponding facts from the finite dimensional differential inclusions theory.
We give a general approach to infinite dimensional non-Gaussian Analysis for measures which need not have a logarithmic derivative. This framework also includes the possibility to handle measures of Poisson type.
For infinite measure-theoretic entropy systems, we introduce the notion of measure-theoretic metric mean dimension of invariant measures for different types of measure-theoretic $\epsilon$-entropies, and show that measure-theoretic metric…
Quasi-invariant and pseudo-differentiable measures on a Banach space $X$ over a non-Archimedean locally compact infinite field with a non-trivial valuation are defined and constructed. Measures are considered with values in $\bf R$.…
Multidimensional scaling (MDS) is a popular technique for mapping a finite metric space into a low-dimensional Euclidean space in a way that best preserves pairwise distances. We study a notion of MDS on infinite metric measure spaces,…
Packing measures and Hewitt-Stromberg measures on products of metric spaces are investigated. New product inequalities for packing and lower packing dimensions are esatblished and used to solve a problem of Hu and Taylor regarding packing…
We discuss various infinite-dimensional configuration spaces that carry measures quasiinvariant under compactly-supported diffeomorphisms of a manifold M corresponding to a physical space. Such measures allow the construction of unitary…
We describe some Cartesian products of metric spaces and find conditions under which products of ultrametric spaces are ultrametric.
We review the present status of gauge theories built on various quantum space-times described by noncommutative space-times. The mathematical tools and notions underlying their construction are given. Different formulations of gauge theory…