If [itex] f \in L^1(0,1) [/itex] and if [itex] \int_0^1 fg = 0 [/itex] for any continuous [itex]g \colon (0,1) \rightarrow \mathbb{R}[/itex], then is it the case that [itex]f = 0[/itex] almost everywhere in [itex](0,1)[/itex]?(adsbygoogle = window.adsbygoogle || []).push({});

Thanks.

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# Integral of product of two functions = 0

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