# Define measure through a measure [closed]

Let us define a measure as follows:

$\nu (B) := \pi^{-d/2} \int_B \exp (-\vert x\vert ^2)\mathrm{d}m^d(x)$ where $m^d$ is the $d$-dimensional Lebesgue measure.

Is there a obvious interpretation of this measure?

## closed as unclear what you're asking by Nate Eldredge, Dominik, Davide Giraudo, Leucippus, NamasteDec 7 '16 at 1:32

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• This is Gaussian measure with mean zero and variance $1/2$. What do you want to know about it? – Nate Eldredge Dec 6 '16 at 15:10
• For the moment that is all I wanted to know, Thanks a lot! Is there also a name for the following measure defined and the sphere $\mathbb{S}^d$: $\nu (A) := \int_A f d \sigma$ where $f$ is an arbitrary fixed continuous function and $\sigma$ is the surface measure? – tubmaster Dec 6 '16 at 15:25
• Please ask that as a new question. Asking new questions in comments is bad practice; people can't find them easily. – Nate Eldredge Dec 6 '16 at 15:44
• ok, done, sorry for that – tubmaster Dec 6 '16 at 15:51

This is Gaussian measure with mean zero and variance $1/2$.