Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let $K(x,\omega) \in C^{\infty}(\Omega \times \Omega)$, where $\Omega$ is a domain in $\mathbb{R}^{n}$. Let $\mu$ be a probability measure on $\Omega$. My question is under which conditions an equality $$ L\int\limits_{\Omega} K(\cdot,\omega) \, \mu(d \omega) = \int\limits_{\Omega} LK(\cdot,\omega) \, \mu(d\omega) $$ holds for any $L \in (C^{\infty}(\Omega))^{*}$?

share|cite|improve this question
Using the notion of the tensor product of distributions it can easy be shown that the equality holds forever. – Nimza May 8 '12 at 13:44

Your Answer


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

Browse other questions tagged or ask your own question.