# terminology clarification needed: projection of a measure to an open set

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?

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