Subsets of vertical planes in the first Heisenberg group

It is shown that if \(A\) is a Borel subset of the first Heisenberg group contained in some vertical subgroup, then vertical projections almost surely do not decrease the Hausdorff dimension of \(A\).

Saved in:
Bibliographic Details
Published in:arXiv.org 2024-07
Main Author: Harris, Terence L J
Format: Article
Language:English
Subjects:
Subgroups
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:It is shown that if \(A\) is a Borel subset of the first Heisenberg group contained in some vertical subgroup, then vertical projections almost surely do not decrease the Hausdorff dimension of \(A\).
ISSN:2331-8422