Hello everybody,

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 gauß-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,

best regards,

slabic