课程名称︰实分析二
课程性质︰数学研究所必选修
课程教师︰刘丰哲
开课学院:理学院
开课系所︰数学系、数学研究所、应用数学科学研究所
考试日期︰2015年03月25日(三),11:20-11:35
考试时限:15分钟
试题 :
实分析(二) 2014学年度
Quiz #1 Let -∞ < a < c < d < b < ∞ and let g be the indicator function of
(c,d).
(1) Find a sequence {gn} of AC functions on [a,b] such that 0≦gn≦1 for all n,
gn(a) = gn(b) = 0 for all n and gn→g a.e. on [a,b]. b
(2) Suppose that f is a AC function on [a,b] such that ∫fg'dλ = 0 for all AC
a
function g on [a,b] such that g(a) = g(b) = 0. Show that f = constant a.e.