Forn‰¥1, letF_nandFbe d.f.s of r.v.s let f_nbe real-valued measurable functions defined on  be continuous, and letg: R †’ [0, ˆž] be continuous, Assume that:

(i) F_n †’ F as n †’ ˆž.

(ii) 

(iii)  uniformly on finite intervals.

(iv)

dF and  g dF < ˆž.

Then show that

Use the Helly-Bray Lemma 

Transcribed Image Text:

R, let f : R → R