Scaled Oscillation and Level Sets

TL;DR

This paper investigates the size and regularity of level sets of continuous functions that exhibit bounded oscillation at different scales, contributing to the understanding of their geometric properties.

Contribution

It introduces new bounds and regularity results for level sets of functions with controlled scaled oscillation, advancing the theoretical understanding of their structure.

Findings

Established bounds on the size of level sets

Proved regularity properties under scaled oscillation constraints

Extended previous results to broader classes of functions

Abstract

We study the size and regularity properties of level sets of continuous functions with bounded upper-scaled and lower-scaled oscillation.