I know that if $X$ and $Y$ are two independent normal random variables defined on the same probability space ($\Omega$, $\cal{F}$,$\cal{P}$), the product may not be normal, but is it possible to construct a new probability space such that $XY$ can be normal in the new probability space? If it is valid, how to construct such new probability space?
I have this question since when I read the proof of Meyer's Inequality using Mathematical Induction, the author seems to use this result to proof it. The book I read is "The Malliavin Calculus and Related Topics" written by David Nualart. Thanks for anyone's help.