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.]*

To express a random variable as the difference of two, I think finite moment is not needed, it is needed when we express expectation as the difference of two.

Thanks.

]]>I have a question. If you are an infinite number of random variables. You can still use the strong law of large numbers? please more explain for me.

best regards ]]>