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

Since 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?