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Euler Measure

Define the Euler measure of a polyhedral set as the Euler Integral of its indicator function. It is easy to show by induction that the Euler measure of a closed bounded convex Polyhedron is always 1 (independent of dimension), while the Euler measure of a $d$-D relative-open bounded convex Polyhedron is $(-1)^d$.




© 1996-9 Eric W. Weisstein
1999-05-25