Related papers: Some Notes on Standard Borel and Related Spaces
These notes are connected to a "potpourri" topics class and deal with some basic issues involving norms and convexity.
In the present note a generalization of Borel-Cantelli Lemma is proposed.
We express the Partial regularities and $a^*$-invariants of a Borel type ideal in terms of its irredundant irreducible decomposition. In addition we consider the behaviours of those invariants under intersections and sums.
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 are expanded notes of a course on basics of quantum field theory for mathematicians given by the author at MIT.
This paper aims to provide a careful and self-contained introduction to the theory of topological degree in Euclidean spaces. It is intended for people mostly interested in analysis and, in general, a heavy background in algebraic or…
These notes are concerned with Abel sums and connections with analytic extensions of Fourier integrals.
Lecture notes on selected topics in the theory of gravitation.
This book provides a gentle introduction to fractional Sobolev spaces, which play a central role in the calculus of variations, partial differential equations, and harmonic analysis. The first part deals with fractional Sobolev spaces of…
This paper is concerned with analysis on metric spaces in a variety of settings and with several kinds of structure.
Our understanding of space and time is probed to its depths by black holes. These objects, which appear as a natural consequence of general relativity, provide a powerful analytical tool able to examine macroscopic and microscopic…
Survey talk on certain aspects of the subject, stressing the neighbor relation as a basic notion in differential geometry.
A variational equation of the third order in three-dimensional space is proposed which describes autoparallel curves of some connection.
These notes are an introduction to some basic aspects of the Castelnuovo-Mumford regularity and related topics such as weak regularity, a*-invariant and partial regularities.
In this paper, we develop an abstract framework for John-Nirenberg inequalities associated to BMO-type spaces. This work can be seen as the sequel of [5], where the authors introduced a very general framework for atomic and molecular Hardy…
We study and describe possibilities for arities of elementary theories and of their expansions. Links for arities with respect to Boolean algebras, to disjoint unions and to compositions of structures are shown. The dynamics for arities of…
We introduce and study properties of certain new harmonic function spaces on products of upper half-spaces.Norm estimates for the so-called expanded Bergman projections are obtained.Sharp theorems on multipliers acting on certain Sobolev…
The article provides a modest survey of the absolute theory of general systems of (partial) differential equations. The equations are relieved of all additional structures and subject to quite arbitrary change of the variables. An abstract…
We present a broad review on black holes. We analyse some of the fundamental concepts in black hole theory, the observational and theoretical status of stellar and galactic black holes, and their appearance as quantum objects.
We review a few useful concepts about polarization measurements in the quantum domain. Using a perfectly general formalism, we show how to build the quantum counterpart of some classical quantities like Stokes parameters and Mueller…