so why not call this article "mutually singular measures" like the first line says? --itaj 04:01, 12 May 2006 (UTC)
let be a measurable space. i'm talking here about real-value signed finite measures on this space. let M be a set of measures.
let N be the set of all measures absolutely continuous with respect to a measure in the linear span of measures in M. i.e.
for a measure i'll denote . the set of measures mutually singular to .
and for a set of measures L. . the set of all measures mutually singular to all measures in L.
my question is if the above implies that i know this is true if there's only one measure in M, but i need to know about infinite set M, countable and bigger. --itaj 04:05, 12 May 2006 (UTC)
- If span is in the sense of vector spaces, then no. Consider . Then or N, but it is in singl(singl(N)). (Cj67 23:39, 25 June 2006 (UTC))