Let denote counting measure and denote Lebesgue measure. What is ?
I am a little fuzzy on the product measure and have tried two ways to do this. Can someone explain why the incorrect version is wrong and the correct version is right?
By definition of the product measure since each and
and . So this value is not well defined. If any of these are right, I would like to know why one is right, the other is wrong. If they are both wrong, I would appreciate an explanation on how to do this properly.