A General Mass Transference Principle

In this paper we prove a general form of the Mass Transference Principle for \(\limsup\) sets defined via neighbourhoods of sets satisfying a certain local scaling property. Such sets include self-similar sets satisfying the open set condition and smooth compact manifolds embedded in \(\mathbb{R}^n\...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2018-08
Main Authors: Demi, Allen, Baker, Simon
Format: Article
Language:English
Subjects:
Self-similarity
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper we prove a general form of the Mass Transference Principle for \(\limsup\) sets defined via neighbourhoods of sets satisfying a certain local scaling property. Such sets include self-similar sets satisfying the open set condition and smooth compact manifolds embedded in \(\mathbb{R}^n\). Our main result is applicable in locally compact metric spaces and allows one to transfer Hausdorff \(g\)-measure statements to Hausdorff \(f\)-measure statements. This work extends previous results of this type in several distinct directions.
ISSN:2331-8422