# Distance-like functions and smooth approximations: a correction to "Logarithm laws for flows on homogeneous spaces"

## TL;DR

This paper corrects a mistake in a previous work on logarithm laws for flows on homogeneous spaces, specifically regarding the approximation of sets by smooth functions.

## Contribution

It provides a correction to a key proposition in Kleinbock and Margulis's 1999 paper, ensuring the validity of their results on logarithm laws.

## Key findings

- Corrected the flawed approximation proposition
- Ensured the validity of logarithm laws for flows on homogeneous spaces
- Clarified the mathematical foundations for future research

## Abstract

One of the propositions in the paper [D. Kleinbock and G.A. Margulis, Logarithm laws for flows on homogeneous spaces, Invent. Math. 138 (1999), 451-494] related to approximating certain sets by smooth functions, was recently found to be incorrect. Here we correct the mistake.