Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $\mu$ a signed measure, and $f$ a integrable function with respect to $|\mu|$, and if $\nu$ is defined for every mensurable set by $$\nu(E) = \int_E f \, d\mu$$

then $\nu \ll \mu$.

I need some tips, because in the exercise I have a hint, that is:

$$\int f \, d\mu = \int f \, d\mu^+ - \int f \, d\mu^-$$

If $\mu$ is a finite signed measure, then, for every measurable set $E$

$$|\mu|(E) = \sup \left|\int_E f \, d\mu \right|$$ where the supremum is extended over all measurable functions $f$ such that$|f| \leq 1$.

In the case that $\mu$ is finite sigbed measure is it solve right? Or there is some things that I forget? Thanks so much

share|improve this question
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.