Does this

Edit: Robin's comments appear to have anything made the matter a lot clearer to do with second-order stationary or some sort of homogeneous distribution of elements of me. I now suppose that the vector space ?

Alternatively, of random variables with zero expectation are there studied in the context of second order stationary processes.

The other question remains: are vector spaces of random variables with non-zero expectation also studied?

Does this have anything to do with second-order stationary or some sort of homogeneous distribution of elements of the vector space?

Alternatively, are there vector spaces of random variables with non-zero expectation?

Does this have anything to do with second-order stationary or some sort of homogeneous distribution of elements of the vector space?

Alternatively, are there vector spaces with non-zero expectation?