1. Let fgng be a sequence of integrable functions which converges a.e. toan integrable function g. Let ffng be a sequence of measurable functionssuch that jf j g and ff g converges 1. Let {gn} be a sequence of integrable functions which converges a.e. toan integrable function g. Let {fn} be a sequence of measurable functionssuch that |fn < gn and {fn} converges to f a.e. Alsolim f gn = f g. Prove that ffn - f| → 0.supposethat%3D

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Description: 1. Let fgng be a sequence of integrable functions which converges a.e. toan integrable function g. Let ffng be a sequence of measurable functionssuch that jf j g and ff g converges 1. Let {gn} be a sequence of integrable functions which converges a

Solution: Given that gn is a sequence of integrable functions which converges a.e. to an integrable…

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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

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

Advanced Engineering Mathematics

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Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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1. Let fgng be a sequence of integrable functions which converges a.e. to an integrable function g. Let ffng be a sequence of measurable functions such that jf j g and ff g converges

1. Let {gn} 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
lim f gn = f g. Prove that ffn - f| → 0.
suppose
that
%3D

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