※ 引述《wyob (Go Dolphins)》之銘言：
: 最近再寫這本
: 有時卡住想上來請教，感謝
: Let g(t) be monotone increasing and absolutely conti. on [a,b]
: let f be bounded and measurable on [c,d],c=g(a),d=g(b)
: then f(g(t)) is measurable on [a,b] and
: d b
: ∫f(x)dx=∫f(g(t))g'(t)dt
: c a
: 需要一點方向阿~~~~
試試看，有錯莫怪。
x
令 F(x) = ∫ f(s) ds => F is a.c. on [c,d]
c
=> F o g is a.c. on [a,b] => F o g is measurable on [a,b]
因為 F'(x) = f(x) a.e. ， 所以 (F o g)'(t) = f(g(t))g'(t) a.e.
d g(b)
∫ f(x)dx = ∫ f(x) dx
c g(a)
= F(g(b)) - F(g(a))
b
= ∫ (F o g)'(t) dt
a
b
= ∫ f(g(t))g'(t) dt
a
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