課程名稱︰分析導論優二
課程性質︰數學系大二必修
課程教師︰王振男
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰2015/05/19
考試時限（分鐘）：35
試題 :
1. (a) (10%) Let {f } be a sequence of Lebesgue integrable function such that f
k k
→ f a.e. with f also integrable. Then ∫|f - f| → 0 iff ∫|f | →
k k
∫|f|.
(b) (10%) Let f be Lebesgue integrable over a measurable set E. Then for any
ε > 0, there is a simple function φ such that ∫|f - φ| < ε.
E