Talk:Weierstrass M-test

From Wikipedia, the free encyclopedia

You have new messages (last change).

I'm reading Complex Analysis by Freitag and Busam, and their version of the Weiestrass M-test say that every normally convergent series converges absolutely and locally uniformly. Their definition of normal convergence also differs with the definition found on Wikipedia. They say that normal convergence of fn: D -> C means that for every a in D, there exists a neighborhood of a, U, such that there exists a sequence (of real numbers) Mn such that for every z in intersection(D, U), abs(fn(z)) < Mn and SUM(Mn) converges.

One thing I'm wondering is, what do they mean by "absolutely convergent". One clue is that they say a consequence of the Weiestrass M-test is that normally convergent series can be arbitrarily reordered without disturbing the limit of the series... Danielx 06:11, 7 March 2007 (UTC)

See absolute convergence. Oleg Alexandrov (talk) 15:34, 7 March 2007 (UTC)
Retrieved from "http://en.wikipedia.org../../../w/e/i/Talk%7EWeierstrass_M-test_6a4a.html"