Presumably is supposed to be a positive Radon measure.
From the definition of the -norm, for almost all t in [a,b]. Then (integral of a constant is the constant times the measure of the interval).
Let C be compakt
a radon measure and .
Do you know how to proof the following inequality:
I don't get it.
By the way I'm not sure about the correctness of this inequaility if is an arbitrary measure. If it's correct where equals the Lebesgue measure, you can use this instead of the Radon measure.
Any comments are welcome