Medida de Haar

Abstract

One of the most useful properties of the measurement of Lebesgue integral is its invariance under translations and rotations. For example, if a ∈ R n, r ∈ R n × n and f is a Lebesgue integrable function on R n, then Z Rn f (x) dx = Z Rn f (rx + a) dx. The notion of Haar measure is a generalization of this example. In this sense in a (more generally locally compact) compact group G, there is a measure m such that ZG f (x) dm (x) = ZG f (bx) dm (x), for an integrable function f on G and element b ∈ G. This measure was introduced by Alfred Haar, Hungarian mathematician, in 1933. "The proof that there is an invariant measure on a locally compact and 'separable group. Later Banach theorem generalizes axiomatically defining congruence. In addition severability it is not essential in the work of Banach, as their arguments are valid by replacing sequential compactness compactness. Finally Haar's theorem was generalized to locally compact groups and completed in 1936 with the uniqueness theorem Von Neumann because "