Haar Measure - Haar Integral

Using the general theory of Lebesgue integration, one can then define an integral for all Borel measurable functions f on G. This integral is called the Haar integral. If μ is a left Haar measure, then

for any integrable function f. This is immediate for indicator functions, being essentially the definition of left invariance.

Read more about this topic:  Haar Measure

Famous quotes containing the word integral:

    “Painting myself for others, I have painted my inward self with colors clearer than my original ones. I have no more made my book than my book has made me—a book consubstantial with its author, concerned with my own self, an integral part of my life; not concerned with some third-hand, extraneous purpose, like all other books.”
    —Michel de Montaigne (1533–1592)