So if we tried to get around requiring , the strong law of large numbers, as stated, would fail.

]]>One thing that’s been bothering me for a while: why is the absolute value sign used in the statement of the theorems? Why do we need E(|X|) instead of just E(X)?

Thank you.

]]>*[Corrected, thanks – T.]*

You wrote: “The concepts of convergence in probability and almost sure convergence in probability theory are specialisations of the concepts of convergence in measure and pointwise convergence almost everywhere in measure theory.”

In measure theory, is there any different between “pointwise convergence almost everywhere” and “convergence almost everywhere”?

*[No – T.]*