课程名称︰分析导论优二
课程性质︰数学系大二必修
课程教师︰王振男
开课学院：理学院
开课系所︰数学系
考试日期（年月日）︰2015/05/19
考试时限（分钟）：35
试题 :
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