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:
“An island always pleases my imagination, even the smallest, as a small continent and integral portion of the globe. I have a fancy for building my hut on one. Even a bare, grassy isle, which I can see entirely over at a glance, has some undefined and mysterious charm for me.”
—Henry David Thoreau (1817–1862)