title: Euler measure
text: # 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 $(-1)^{d}$.
  
  