Hello!

I'm trying to show that if f is a measurable function on some space X, and if

then

In other words, trying to show f is real-valued (not infinity) mu-almost everywhere.

I thought maybe the contrapostive would work, ie,

Presume .

Call the set (for "big" valued, hehe)

Then

If I can just show , then since ,

as well.

So I am just wondering if the above looks alright, and what's left is how to possibly show that for and ?!

Thanks very much!