Euler measure

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

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]

• Measure theory

• Exponentiation and Euler measure

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