Give an example in of a sequence of measurable functions such that but does not converge to zero a.e.
For this one, I can't think of a sequence that fits this criteria. What would this sequence look like? I can't think of one right now.
Give an example in of a sequence of measurable functions such that but does not converge to zero a.e.
For this one, I can't think of a sequence that fits this criteria. What would this sequence look like? I can't think of one right now.
Have a look at this:
Choose a sequence in and real numbers such that every belong to infinitely many intervals .
For instance, , etc. (dyadic points) and ,...
Then let .
There may be simpler, that's what came to my mind. Since can't be monotonic, it must look like my example anyway.