Weierstrass M-test

Let X be any set, {fn}n a sequence of real or complex valued functions on X and {Mn}n a sequence of non-negative real numbers. Suppose that, for each n and xX, we have |fn(x)|Mn. Then f=n=1fn converges uniformly if n=1Mn converges.

Title Weierstrass M-testMathworldPlanetmathPlanetmath
Canonical name WeierstrassMtest
Date of creation 2013-03-22 12:56:11
Last modified on 2013-03-22 12:56:11
Owner yark (2760)
Last modified by yark (2760)
Numerical id 13
Author yark (2760)
Entry type Theorem
Classification msc 30A99
Related topic AbsoluteConvergence