On the Measure of sets of parallel linear subspace in affine space

Abstract

Demostració d'un teorema relacionat amb la mesura dels conjunts del subespai lineal paral·lel a l’espai afí

The aim of this paper is to prove the following theorem: “in order that sets of elements H composed by q parallel linear subspaces of dimensions h1, h2… Hq, which transform transitively by the unimodular affine group ʮ have an invariant measure with respect to ʮ, it is necessary and sufficient that the dimensions hi be all equal, h1 = h2 = h3 = … = hq = h, and that q = n + 1 – h”