Existence of $x$
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- Posts: 10
- Joined: Mon May 30, 2016 9:19 pm
Existence of $x$
Let $A \subseteq \mathbb{R}^n$ be a compact and connected subset of $\mathbb{R}^n$. Suppose that $f:A \rightarrow \mathbb{R}$ is a continuous function and $g:A \rightarrow \mathbb{R}$ an integrable one. Prove that there exists an $x$ such that
$$\int \limits_A f g = f(x) \int \limits_A g $$
$$\int \limits_A f g = f(x) \int \limits_A g $$
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- Posts: 16
- Joined: Fri Aug 12, 2016 4:33 pm
Re: Existence of $x$
What if $ \int _{A}g=0$ and $ \int _{A}fg\neq 0 $ ?
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