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In fact i believe (at least it should be) that if [tex] f_{n} (x) [/tex] and [tex] g_{n} (x) [/tex] are a succesion of function for [tex] n \rightarrow \infty [/tex] then the product of the 2 sucessions should be equal to the product of the 2 distributions..

hence [tex] f_{n} (x) \rightarrow d(x) [/tex] and [tex] g_{n} (x) \rightarrow e(x) [/tex] where d(x) and e(x) are 2 distributions then :

[tex] f_{n} (x) g_{n} (x) \rightarrow d(x)e(x) [/tex] ?

I have read about 'MOllifiers' and several methods for generalizing the distribution theory to include product of distributions, also couldn't the product be always defined as a 'sum' (in fact the sum of 2 distributions is defined) since:

[tex] a X b = a+a+a+a+a+a+a+a+... [/tex] (the sum has 'b' terms)

or [tex] log(a X b )=log(a) +log(b) [/tex] :Grumpy: