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Stupid Question: If I'm given a non-euclidean space, such as $S^n $ (n-dimensional unit sphere), with the the uniform measure $\mu$ on it.

I'm also given a function $f:S^n \to \mathbb{R} $ that is bounded, by a constant $C$ . As an analogous to the Lebesgue measure case, can I say that: $ \int_{S^n } f d\mu \leq C \mu ( S^n) = C $?

Hope you'll be able to help

Thanks !

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    Yes. This follows from the fact that the integral of a non-negative function is non-negative and is true for any measure on any measure space whatsoever.2012-07-22
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    Great! THanks a lot !2012-07-22

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