Tangent measures of non-doubling measures

TL;DR

This paper constructs a non-doubling measure on the real line whose tangent measures are all equivalent to Lebesgue measure, challenging assumptions about measure doubling properties.

Contribution

It introduces a novel non-doubling measure with tangent measures equivalent to Lebesgue measure, providing new insights into measure theory.

Findings

Constructed a non-doubling measure on the real line

All tangent measures are equivalent to Lebesgue measure

Challenges existing assumptions about measure doubling

Abstract

We construct a non-doubling measure on the real line, all tangent measures of which are equivalent to Lebesgue measure.