Relationship To Other Areas of Mathematics
Of particular importance in harmonic analysis are the locally compact groups, because they admit a natural notion of measure and integral, given by the Haar measure. The theory of group representations is almost identical for finite groups and for compact topological groups. In general, σ-compact Baire topological groups are locally compact.
Read more about this topic: Topological Group
Famous quotes containing the words relationship to, relationship, areas and/or mathematics:
“Whatever may be our just grievances in the southern states, it is fitting that we acknowledge that, considering their poverty and past relationship to the Negro race, they have done remarkably well for the cause of education among us. That the whole South should commit itself to the principle that the colored people have a right to be educated is an immense acquisition to the cause of popular education.”
—Fannie Barrier Williams (1855–1944)
“Every relationship that does not raise us up pulls us down, and vice versa; this is why men usually sink down somewhat when they take wives while women are usually somewhat raised up. Overly spiritual men require marriage every bit as much as they resist it as bitter medicine.”
—Friedrich Nietzsche (1844–1900)
“The ambiguous, gray areas of authority and responsibility between parents and teachers exacerbate the distrust between them. The distrust is further complicated by the fact that it is rarely articulated, but usually remains smoldering and silent.”
—Sara Lawrence Lightfoot (20th century)
“Why does man freeze to death trying to reach the North Pole? Why does man drive himself to suffer the steam and heat of the Amazon? Why does he stagger his mind with the mathematics of the sky? Once the question mark has arisen in the human brain the answer must be found, if it takes a hundred years. A thousand years.”
—Walter Reisch (1903–1963)