(Note that I am interested in the Gelfand-Pettis integral specifically, as opposed to, for example, the Bochner integral.) I have tried Googling things like "integral topological vector space", ...
What is the notion of a principal value of an integral when the singularity appears at one endpoint? Namely, $ PV \int_a^b f(t) dt = ? $, where the integral is convergent in the upper limit, but ...
I imagine most people who frequent MO have been indoctrinated into the point of view that the Riemann integral can be safely discarded once one has taken the time to develop the Lebesgue integral. ...
Note: I first posted question on math.stackexchange and I got one reply, which was a bit helpful (I'm still trying to understand it fully), but did not explore the two solution cases that I mentioned. ...
(Note: I asked this question a few days ago on math.stackexchange but didn't get any responses. I've therefore decided to post it here instead.) I have a problem justifying the throwing away the ...