Timeline for Is P(X) a connected set for a set X with a $\sigma$-algebra P(X) and a measure function m on it to [0,$\infty$] when P(X) is equiped with meter d, that for every A,B in P(X), $d(A,B)=m(A \Delta B)$?

11 events

when toggle format	what		by	license	comment
Nov 13, 2012 at 19:27	vote	accept	AmirHosein Sadeghimanesh
Nov 13, 2012 at 19:23	vote	accept	AmirHosein Sadeghimanesh
Nov 13, 2012 at 19:27
Nov 13, 2012 at 19:22	vote	accept	AmirHosein Sadeghimanesh
Nov 13, 2012 at 19:23
Nov 13, 2012 at 19:22	vote	accept	AmirHosein Sadeghimanesh
Nov 13, 2012 at 19:22
Nov 12, 2012 at 14:03	comment	added	Pietro Majer		by the way, the term "atomless" is better than the unclear "non-atomic" (="no atoms at all", or "not atoms only"?), which is also a funny litotes. I'll correct now.
Nov 9, 2012 at 13:13	comment	added	Andreas Blass		As far as I can see, the revised version of the question was already answered affirmatively (before the revision) by Pietro Majer, since Lebesgue measure on a (measurable) subset of the reals is always atomless.
Nov 9, 2012 at 13:06	history	edited	AmirHosein Sadeghimanesh	CC BY-SA 3.0	added 589 characters in body
Nov 7, 2012 at 17:19	answer	added	Pietro Majer		timeline score: 5
Nov 7, 2012 at 17:06	comment	added	Davide Giraudo		Not necessarily, for example $X=\Bbb N$,the set of natural numbers, with counting measure. Then \{\emptyset\}$ is open, and so is $\{A\subset \Bbb N,A\neq\emptyset\}=\{A,d(A,\emptyset)>0\}$.
Nov 7, 2012 at 17:05	comment	added	Davide Giraudo		Not necessarily, for example $X=\Bbb N, the set of natural numbers, with counting measure. Then $\{\emptyset\}$ is open, and so is $\{A\subset \Bbb N,A\neq\emptyset\}=\{A,d(A,\emptyset)>0\}$.
Nov 7, 2012 at 16:52	history	asked	AmirHosein Sadeghimanesh	CC BY-SA 3.0