Related papers: Some Notes on Standard Borel and Related Spaces

We introduce a notion of relative primeness for equivalence relations, strengthening the notion of non-reducibility, and show for many standard benchmark equivalence relations that non-reducibility may be strengthened to relative primeness.…

A concise introduction to the Standard Model of fundamental particle interactions is presented.

In this lecture notes we try to familiarize the audience with the theory of Bernoulli polynomials; we study their properties, and we give, with proofs and references, some of the most relevant results related to them. Several applications…

In this note we briefly survey and propose some open problems related to isoparametric theory.

We obtain formulas for the coefficients of positive and negative powers of a partial theta function.

Lindel\"of spaces are studied in any basic Topology course. However, there are other interesting covering properties with similar behaviour, such as almost Lindel\"of, weakly Lindel\"of, and quasi-Lindel\"of, that have been considered in…

This paper surveys some recent developments in measures of association related to a new coefficient of correlation introduced by the author. A straightforward extension of this coefficient to standard Borel spaces (which includes all Polish…

These informal notes briefly discuss various aspects of Cantor sets.

In these notes we focus on commutative finite-dimensional normed algebras and some basic examples.

We introduce the notion of an approximation system as a generalization of Taylor approximation, and we give some first examples. Next we develop the general theory, including error bounds and a sufficient criterion for convergence. More…

This is an expository introduction to simplicial sets and simplicial homotopy theory with particular focus on relating the combinatorial aspects of the theory to their geometric/topological origins. It is intended to be accessible to…

A very elementary introduction to quantum algebras is presented and a few examples of their physical applications are mentioned.

Lecture-notes: introducing and discussing basic kp concepts related to bands interaction at an elementary level to beginners

The present note contains a review of $p$-energies and Sobolev spaces on metric measure spaces that carry a strongly local regular Dirichlet form. These Sobolev spaces are then used to generalize some basic results from the calculus of…

In this note some philosophical thoughts and observations about mathematics are expressed, arranged as challenges to some common claims.

In this paper, we present the classification of generalized Wallach spaces and discuss some related problems.

After a short review of the historical milestones on normal numbers, we introduce the Borel numbers as the reals admitting a probability function on their different bases representations. In this setting, we provide two probabilistic…

Here I share a few notes I used in various course lectures, talks, etc. Some may be just calculations that in the textbooks are more complicated, scattered, or less specific; others may be simple observations I found useful or curious.

These informal notes deal with Fourier series in one or more variables, Fourier transforms in one variable, and related matters.

This is the first of two works concerning the Sobolev calculus on metric measure spaces and its applications. In this work, we focus on several notions of metric Sobolev space and on their equivalence. More precisely, we give a systematic…