Suppose is a non-negative integrable function on .For each ,define .
Show that .
( is the measure of .)
I was trying to prove that since is integrable,then .Since is a decreasing sequence of sets,so
so and hence get the result.
but the problem is I have to assume to claim the result.I was stuck here.
Can anyone help?Or if this is not the correct approach,can anyone show me the right way?