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[edit]

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 ${\displaystyle (-1)^{d}}$.^[1]

See also[edit]

• Measure theory

Notes[edit]

External links[edit]

• Exponentiation and Euler measure

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