Transverse invariant measures extends to the ambient space

TL;DR

This paper demonstrates that transverse invariant measures in foliated spaces can be extended to measures on the entire ambient space, broadening the understanding of measure theory in foliation contexts.

Contribution

It introduces a method to extend transverse invariant measures to the ambient space, providing a new perspective in the study of foliated spaces.

Findings

Transverse invariant measures can be extended to the ambient space.

The extension preserves invariance properties.

This approach simplifies analysis of measures in foliated structures.

Abstract

It is shown that any transverse invariant measure of a foliated space can be considered as a measure on the ambient space.