# Conical upper density theorems and porosity of measures

## TL;DR

This paper investigates the distribution of measures with finite lower density around lower-dimensional planes in Euclidean space, exploring their relation to porosity and applicable to various Hausdorff and packing measures.

## Contribution

It establishes new connections between conical upper density theorems and porosity, extending their applicability to a broad class of measures.

## Key findings

- Measures with finite lower density are distributed around (n-m)-planes in small balls.
- Relations between conical upper density theorems and porosity are clarified.
- Results apply to many Hausdorff and packing measures.

## Abstract

We study how measures with finite lower density are distributed around $(n-m)$-planes in small balls in $\mathbb{R}^n$. We also discuss relations between conical upper density theorems and porosity. Our results may be applied to a large collection of Hausdorff and packing type measures.