What is meant by space average?

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What is meant by "space average?"

What is meant by the term "space average?"


I think my understanding would be similar to taking the time average of something, i.e. using an integral:
\frac{1}{b-a}*\int f(t) dt

Where the integral goes from a to b.

But instead t would be replaced with x (the position), and the function adjusted appropriately. Is this right?
 
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Yes it is, at least for 1-dimensional space.
 
It's given a gas of particles all identical which has T fixed and spin S. Let's ##g(\epsilon)## the density of orbital states and ##g(\epsilon) = g_0## for ##\forall \epsilon \in [\epsilon_0, \epsilon_1]##, zero otherwise. How to compute the number of accessible quantum states of one particle? This is my attempt, and I suspect that is not good. Let S=0 and then bosons in a system. Simply, if we have the density of orbitals we have to integrate ##g(\epsilon)## and we have...
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