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:
“Film music should have the same relationship to the film drama that somebody’s piano playing in my living room has to the book I am reading.”
—Igor Stravinsky (1882–1971)
“Harvey: Oh, you kids these days, I’m telling you. You think the only relationship a man and a woman can have is a romantic one.
Gil: That sure is what we think. You got something better?
Harvey: Oh, romance is very nice. A good thing for youngsters like you, but Helene and I have found something we think is more appropriate to our stage of life—companionship.
Gil: Companionship? I’ve got a flea-bitten old hound at home who’ll give me that.”
—Tom Waldman (d. 1985)
“In my writing I am acting as a map maker, an explorer of psychic areas ... a cosmonaut of inner space, and I see no point in exploring areas that have already been thoroughly surveyed.”
—William Burroughs (b. 1914)
“It is a monstrous thing to force a child to learn Latin or Greek or mathematics on the ground that they are an indispensable gymnastic for the mental powers. It would be monstrous even if it were true.”
—George Bernard Shaw (1856–1950)