Re: Is there an analog of the central limit theorem for integrals?

Thank you very much for your response.

There certainly is such an analog, and even more, to sums
of dependent random variables. The condition for
asymptotic
normality depends on what are called "strong mixing"
conditions, and there is much literature on this.

Can you (or anyone) elaborate on this? I'd like to look for some literature, but it'd be nice to have something more specific to look for. Will searching for "strong mixing" suffice, or is there some theorem with someone's name attached to it that is the important result for the normality of integrals like the one I describe above?

Thank you.
.