Hello. I am working on the following problem:

Let be a measure space and let be an extended real-valued -measurable function on such that . Show that .

Now, I let and tried to consider the inequalities

The expression on the left side is finite, but as far as I can tell, this doesn't give much information about the expression on the right. At this point, I'm at a loss on this problem, so I would appreciate if anybody had some suggestions.

Thanks.