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 !