How to show that $L^p$ norm is monotone increasing? No, I am not assuming that $\mu$ is a probability measure Actually, that is a good point - I have read that the reverse inequality holds in $\ell^p$ spaces (sequence spaces)
Monotone class theorem vs Dynkin $\pi-\lambda$ theorem Good I was confused because my book calls the first "Monotone class theorem" Also on the wiki page the proof was the same of the one reported on my book (and it was therefore proving, instead of the monotone class theorem, the dynkin $\pi-\lambda$ theorem) I edited the proof out of the wiki page in the meanwhile :-) Thank you!