Euler measure
# Euler measure

In measure theory, the Euler measure of a polyhedral set equals the Euler integral of its indicator function.

## The magnitude of an Euler measure

By induction, it is easy to show that independent of dimension, the Euler measure of a closed bounded convex polyhedron always equals 1, while the Euler measure of a d-D relative-open bounded convex polyhedron is $(-1)^{d}$.

