Viewing topic: Mean Convergence

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Mean Convergence

  • Definition: Let {f_n} be a sequence of Riemann-integrable functions defined on [a,b]. Assume that f is an element of R on [a,b]. The sequence {f_n} is said to converge in the mean to f on [a,b], and we write l.i.m. f_n = f (as n goes to infinity) on [a,b], if limit(inegral_(from a to b) of |f_n(x) - f(x)|^2 dx) = 0 as n goes to infinity.

    Source: Mathematical Analysis, second edition by Tom M. Apostol

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