Vitushkin-type theorems

TL;DR

This paper establishes Vitushkin-type estimates for subsets of Euclidean space with the Gabrielov property, providing concrete examples involving sub-level sets of specific function classes.

Contribution

It introduces Vitushkin-type theorems for sets with the Gabrielov property and offers explicit examples involving sub-level sets of certain functions.

Findings

Vitushkin-type estimates hold for sets with the Gabrielov property.

Concrete examples are provided for sub-level sets of specific functions.

The results extend understanding of geometric properties of such sets.

Abstract

It is shown that for a subset $A\subset\R^n$ that has the global Gabrielov property, a Vitushkin-type estimate holds. Concrete examples are given for sub-level sets of certain classes of functions.