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）︰2015/04/21
考试时限（分钟）：40
试题 :
n
1. (10%) Let V be an open set of |R and φ is a coordinates fransform in V.
Then
Vol(φ(B (x )))
r 0
lim ──────── = |Δ (x )|.
r→0+ Vol(B (x )) φ 0
r 0
n n
2. (10%) Given any set E of |R and d ∈ |R . Define E = {x+d: x∈E}. Show that
d
|E | = |E| , i.e., the outer measure is translation invariant.
d e e