Divide , and . Both sets are measurable. Show that is integrable both in and because it is dominated by the identically 1 function in (which is of finite measure) and by in , integrable by hypothesis.
The question is:
Show that if equals 0 outside a bounded interval and , then
It doesn't appear so difficult, but i dont know how to progress in it. I say let I be the bounded interval, then how do i progress from here? i dont know how to get from this! thanks