Problem 4 (10pt). Let E C R* be a measurable set and f1, f2, ... be a sequence of real-valued measurable functions defined on E. Suppose that for all x E E, lim fn(x) exists. Define the n-+00 function fo : E - R by fo(x) := lim fn(x). n-+00 Show that fo(x) is measurable. Hint: verify that 00 00 00 {xEElfo(x) > c} = UU QxeElf(x)>ctill. i=1l=In=e