1. Let {9n} be a sequence of integrable functions which converges a.e. to an integrable function g. Let {fn} be a sequence of measurable functions such that |fn< gn and {fn} converges to f a.e. Also suppose that lim f gn = S g. Prove that f |fn – f| → 0. %3D

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.