I do not understand an argument in a paper and I hope you could help me.
It is an application of the central limit theorem and I think it is not that difficult.
Consider the two-point spaces
with prob meas.
Furthermore let be the coord.fct., i.e.
Now we want to examine the convergence(k-> infinity) of
For this purpose we set and consider functions of the form
According to the paper, it should now be obvious that the central limit theorem implies the convergence(for k -> ) of this integral to the integral
is the gau▀-measure.
I see roughly the connection between the statement and the CLT, but I am not really able to prove this. I would be pleased, if anybody could help me,