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）︰2015/04/21
考試時限（分鐘）：40
試題 :
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