Definition 8.2.8: Convergence Almost Everywhere

A sequence fn defined on a set D converges (pointwise or uniformly) almost everywhere if there is a set S with Lebesque measure zero such that fn converges (pointwise or uniformly) on D \ S. We say that fn converges (pointwise or uniformly) to f a.e.

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Interactive Real Analysis, ver. 1.9.5
(c) 1994-2007, Bert G. Wachsmuth
Page last modified: Mar 28, 2007