Hi i have a question about [itex]L^2[/itex] spaces and convergence.(adsbygoogle = window.adsbygoogle || []).push({});

Here it goes:

Let [itex]K\subset \mathbb{R}^2[/itex] be bounded.

Let [itex]g,h\in L^2(K)[/itex], and a sequence [itex]f_n\in L^2(K)[/itex] such that [itex]f_n[/itex] converges strongly to [itex]f\in L^2[/itex].

Is it true that [itex]\lim_{n\rightarrow \infty} \int_{K} f_n g h = \int_{K} f g h[/itex]? If it is how?

Thank you.

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# Square integrable functions

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