Title

The set of singularities of regulated functions in several variables

Document Type

Article

Publication Date

9-1-2012

Abstract

We consider a class of regulated functions of several variables, namely, the class of functions f defined in an open set U ⊂ ℝ n such that at each x 0 ∈ U the "thick" limit, exists for all w ∈ S, the unit sphere of ℝ n. We study the set of singular points of f, namely, the set of points S where the thick limit is not constant. In one variable it is well known that S is countable. We give examples where S is not countable in ℝ n, but we prove that if all the thick values are continuous functions of w, then S must be countable. We also consider regulated distributions, elements of the space D′ (U) for which the thick value exists, as a distributional limit, and show that in this case the continuity of the thick values gives the countability of S as well. © 2011 Universitat de Barcelona.

Publication Source (Journal or Book title)

Collectanea Mathematica

First Page

351

Last Page

359

This document is currently not available here.

Share

COinS