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Results tagged with measure-theory
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user 18474
Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.
3
votes
1
answer
277
views
Signed measure that is positive over convex sets
I have a signed measure $\mu$ on a convex subset $C\subset \mathbb{R}^n$, and I want to prove that $\mu$ is a probability measure, most importantly that it is positive everywhere.
I do know that $\in …
10
votes
1
answer
3k
views
Extreme points of a set of probability measures
Consider the set of Borel-measurable probability measures over the interval $[0,1]$ with a given mean, say 1/2. To be precise, I'm talking about the following set $$M=\left(\mu\in \Delta([0,1]):\int x …
3
votes
Reference for a strong intermediate value theorem for measures
There's a stronger version of that (basic) theorem due to Lyapunov. It is stronger because it concerns vectors of measures, and not only a single measure. It states that given a non-atomic vector meas …