※ 引述《wyob (Go Dolphins)》之铭言： : ∞ : (2)f is integrable over [1,∞) if and only if Σ An converges absolutely? : n=1 : 2.Let f be a nonnegative measurable function on R.Show that : n : lim ∫ f=∫f : n→∞ -n R Let fn=f1_[-n,n]. Since f is nonnegative, fn >=0 and is increaing to f a.s. by monotone conv. thereom n lim ∫ f = lim ∫ fn = ∫ lim fn = ∫ f n→∞ -n n→∞ n→∞ R --

※ 发信站: 批踢踢实业坊(ptt.cc) ◆ From: 140.113.5.172