Could someone please give me a simple explanation of when it is valid to interchange the order of Intergration and summation when the summation is an infante summation?
for some context during lecture the other day my current prof interchanged the order, and I asked if that were valid here and he said he couldn't think of any reason it wouldn't be so I said that I remembered a theorem about when that was valid. After class I told him i thought it was fubini's theorem and that the "function" inside the summation had to be Lebesgue integrable and he didn't know what that meant.
if someone could try to help me understand this and to explain the concept to him that would be very helpful.