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 and/or areas:
“Women, because of their colonial relationship to men, have to fight for their own independence. This fight for our own independence will lead to the growth and development of the revolutionary movement in this country. Only the independent woman can be truly effective in the larger revolutionary struggle.”
—Women’s Liberation Workshop, Students for a Democratic Society, Radical political/social activist organization. “Liberation of Women,” in New Left Notes (July 10, 1967)
“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)
“If a walker is indeed an individualist there is nowhere he can’t go at dawn and not many places he can’t go at noon. But just as it demeans life to live alongside a great river you can no longer swim in or drink from, to be crowded into safer areas and hours takes much of the gloss off walking—one sport you shouldn’t have to reserve a time and a court for.”
—Edward Hoagland (b. 1932)