→ ericakk :謝謝您^___^ 02/23 22:47
※ 引述《ericakk (代買IPSA單品8折)》之銘言：
: 小妹在看Bartle的實變
: 對於兩段課文不是很清楚 以下兩個黃色部分 麻煩大家了..謝謝..：
: 1. An ordered pair (χ,Χ) consisting of a set χ and a σ-algebra Χ of
: subsets of χ is called a measurable space.
: Let χ be the set Ｒ of real numbers.
The Borel algebra is the σ-algebra Ｂ generated by all open intervals
(a,b) in Ｒ.
Observe that the Borel algebra Ｂ is also the σ-algebra generated by
all closed intervals [a,b] in Ｒ.
Any set in Ｂ is called a Borel set.
: 對此敘述沒有什麼概念,可否用比較簡單的話講解一次,謝謝...
:
An open set can be represented by a countable union of closed sets.
So, the algebra generated by open sets is equivalent to that generated by
closed sets. Vice versa.
Borel algebra contains "sets". Define those sets to be Borel sets.
: 2. We don't define quotients when the denominator is ±∞.
: 這個我想知道為什麼？因為我在微積分學到 x/±∞ = 0,怎在實變世界就沒定義？
: 謝謝你們^^
I want to know this as well. :P
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◆ From: 124.8.83.5
※ 編輯: emind 來自: 124.8.83.5 (02/22 20:00)