On the packing dimension of projected measures

TL;DR

This paper investigates how the packing dimension of Borel measures behaves under orthogonal projections, establishing conditions for full dimension and bounds, influenced by the support's Assouad dimension, with applications to fractional Brownian motion.

Contribution

It provides a necessary and sufficient condition for typical projections to have full packing dimension and links the support's Assouad dimension to projected measure behavior.

Findings

Typical projections of measures can have full packing dimension under certain conditions.

The Assouad dimension of the support affects the projected measures.

Results extend to images under fractional Brownian motion.

Abstract

We study the packing dimension of Borel measures under orthogonal projections. We give a necessary and sufficient condition such that typical projections of Borel probability measures have full packing dimension and derive general lower bounds in the complementary case. Our approach shows that the Assouad dimension of the support influences the behavior of projected measures. The same method yields corresponding results for images under fractional Brownian motion.