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

I'm reading in Doobs "Classical Potential Theory and its Probabilistic Counterpart" and I'm having trouble with terminology. Specifically, in Part I chapter 6, he talks about

  • the projection of a signed measure $\mu$ to a set $D$ -- I' getting the impression this is just the measure $\mu_D$, the measure $\mu$ restricted to $A$, that is $\mu_D(A) := \mu(D\cap A)$. Is this correct, or is there more to it?
  • the closed support of a measure $\mu$ on $X$. I do know what the support of a measure with a topology $\cal T$ on $X$ is, e.g. (according to Federer's GMT): $$ \mbox{supp}(\mu) := X - \cup\{V: V\in {\cal{T}} \quad \mu(V)=0\} $$ (which is closed by definition). Is there some special meaning hidden when he talks about the "closed support", or is this just it?

I do own some (old, but Doob's book is old, too, in comparison) textbooks covering measure theory (mostly biased somewhat towards real analysis), which do not define these terms -- in what corner of math specialization are these used? Stochastics?

share|cite|improve this question

Your Answer


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