So far, things seem clear to me. My question is the following: Though it makes intuitive sense, how can we be sure that
for all integrable functions g? In the top answer to the question I linked to above, the following claim is made:
For every integrable g, the following formula holds:
It therefore seems that a justification/proof of this claim would answer my question.
I have been exposed to some measure theory and integration theory a few years back, and as I was revising some material recently, this claim was not clear to me. Perhaps this claim is obvious, and my confusion simply arises from a poor understanding of important definitions. Either way, any help in understanding this claim is much appreciated.