Hi there

Let C be compakt

$\displaystyle \mu$ a radon measure and $\displaystyle \mu(C) < \infty$.

Let $\displaystyle v \in L^1(\mathbb{R}) , \ 0 < a < b < \infty$

Do you know how to proof the following inequality:

$\displaystyle \int_{a}^b |v| d\mu \le \mu([a,b]) \cdot \|v\|_\infty$

I don't get it.

By the way I'm not sure about the correctness of this inequaility if $\displaystyle \mu $ is an arbitrary measure. If it's correct where $\displaystyle \mu $ equals the Lebesgue measure, you can use this instead of the Radon measure.

Any comments are welcome

Yours Rapha