On the density at infinity of definable functions

TL;DR

This paper proves that the density at infinity of fibers of a definable function is locally Lipschitz outside a specific set of asymptotic critical values, providing a simplified proof of this property.

Contribution

The paper offers a straightforward proof of the Lipschitz continuity of fiber densities at infinity for definable functions, clarifying their asymptotic behavior.

Findings

Density at infinity of fibers is locally Lipschitz outside asymptotic critical values

Simplified proof of a key property in definable functions

Clarification of asymptotic behavior of fibers

Abstract

In this paper, we give a simple proof that the density at infinity of fibers of a definable function is locally Lipschitz outside the set of asymptotic critical values.