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）︰2015/06/16
考试时限（分钟）：30
试题 :
1
1. (20%) Let f ∈ L [0, 2π] and be periodic of period 2π. For x ∈ |R, we
assume that both f(x+) and f(x-) exists and, furthermore, there exists a
constant C such that
|f(y) - f(x+)| ≦ C(y-x) if y > x
|f(y) - f(x-)| ≦ C(x-y) if y < x
for all y near x. Then
f(x+) + f(x-)
s (x) → ─────── as n → ∞.
n 2