View source for Talk:Borel measure


This was quite demanding: the terminology is very different according to different authors and I tried to be as complete as possible. In fact, since I know quite well the books using terminologies (B) and (C) I could provide precise references, whereas I lack knowledge of the (A)-terminology (the one used in the original article): any suggestion for precise references?[[User:Camillo.delellis|Camillo]] 11:06, 15 August 2012 (CEST)

:Indeed, encyclopedia tends to combine different approaches that often do not meet otherwise... --[[User:Boris Tsirelson|Boris Tsirelson]] 11:16, 15 August 2012 (CEST)

Also, I decided to completely leave out the following comment at the bottom of the original article:

''Often, by the Borel measure on the real line one understands the  measure defined on the Borel sets such that its value on an arbitrary  segment is equal to the length of that segment.''

This statement looks really weird to me: I think nowadays everybody calls it Lebesgue measure, even if one restricts it to the Borel sets... or am I missing something? [[User:Camillo.delellis|Camillo]] 11:06, 15 August 2012 (CEST)

:I agree. Really, when I have to be precise, I call it "Lebesgue measure restricted to Borel sets". --[[User:Boris Tsirelson|Boris Tsirelson]] 11:16, 15 August 2012 (CEST)

===Borel regular measures===

"'''(C)''' Borel (outer) measures such that for any $A\subset X$ there  is a Borel set $B$ with $\mu(A)=\mu(B)$ (cp. with Definition 1.5(3) of  {{Cite|Ma}})." — ?? Hope the Def in Ma is not exactly this. "$\mu(A)=\mu(B)$" does not mean much without something like "$A\subset B$" or "$B\subset A$"... --[[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 14:05, 23 September 2012 (CEST)