Definition talk:Measure (Measure Theory)

I'm unfamiliar with this area of mathematics, but is this definition related to Lebesgue Measure? If so we might consider merging them - if not, then we might want to set up a disambiguation page. KUTGW! --Prime.mover 05:37, 26 August 2009 (UTC)

I wouldn't say they're very closely related as definitions, but in my limited experience "measure" is sometimes used in introductory analysis courses synonymously with "Lebesgue measure," so a disambiguation page wouldn't be inappropriate. Mag487 06:13, 26 August 2009 (UTC)

It's a consequence of the axioms that the measure of a null set is zero, not an additional axiom. Mag487 06:26, 21 August 2010 (UTC)


 * Not sure I understand - I never posited that Measure of Empty Set is Zero, I just invoked it as an elementary consequence. What I did add as axiomatic was:


 * $(3)$: There exists at least one $A \in \mathcal A$ such that $\mu \left({A}\right)$ is finite.


 * Can it be demonstrated that this is itself not axiomatic? Because that's the statement you removed. --prime mover 07:08, 21 August 2010 (UTC)

When the codomain is restricted to be $\R$, one talks about a finite measure; for example, $lambda(\R) = \infty$ where $\lambda$ is the usual measure on $\R$ (Lebesgue measure). Contrary to what is asserted, this certainly doesn't follow from the current statement (maybe because I removed the explicit '$\mu$ is a real-valued function' just a moment ago, but it was necessary anyway). --Lord_Farin 05:10, 16 March 2012 (EDT)