Let f be a nonnegative integrable function on measureable space (X,v). Then tv ({x: f (x)>t}) converges to 0, as t goes infinity.
I want to prove this statement. I got that v ({x: f (x)>t}) goes to zero as t goes infinity. But I cannot prove the full statement.
If tv ({x: f (x)>t}) goes to zero, g (t)v ({x: f (x)>t}) converges to zero whenever g (t)t}) converges to zero or not for g (t)>t. I want to know significant difference of g (t) from t, not the form the constant times t.
Please anyone help me.