※ 引述《wyob (Go Dolphins)》之銘言：
: ∞
: (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
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01/02 22:46, , 1F
01/02 22:46, 1F
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