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May
7
comment What exactly is a probability measure in simple words?
@user13985 - glad it was helpful! Hope it is useful for understanding the more technical definitions...!
May
7
comment What exactly is a probability measure in simple words?
@Berci - yes, and it's necessary for my example! (I tried to edit to make it more clear.) You can't get items of measure zero to "add up" to something like $0.2$ unless you take uncountably many of them together in a set.
May
7
revised What exactly is a probability measure in simple words?
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May
7
answered What exactly is a probability measure in simple words?
Apr
27
answered Ranked Preference Matching Algorithm
Apr
27
comment Can game theory model altruistic behaviour?
Evolutionary game theory studies this question in large part, although not so much from the perspective of your example. The keyword here is "reciprosity" in evolutionary dynamics and evolutionary game theory. I posted some links as a comment on the posted answer also; hope they are interesting/useful!
Apr
27
awarded  Critic
Apr
27
comment Can game theory model altruistic behaviour?
"This is not mathematics." I disagree. In fact, the title question ("Can game theory model altruistic behavior") is a substantial portion of the field of evolutionary game theory. Begin with the wikipedia page on reciprosity, consider Nowak's book, and for examples e.g. this paper or this one.
Apr
21
revised A condition that balls have finite measure
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Apr
20
comment Looking for a probability distribution in $\mathbb{R}^n$: exponentially decreasing density as distance from point
Thanks, I was missing the keyword 'multivariate' which could be very helpful! I cannot tell yet if any of the distributions mentioned in your links are equivalent to the one I'm looking for (since they don't give much geometric intuition and mainly just give the characteristic function), so any thoughts on that would be very helpful!
Apr
20
revised A condition that balls have finite measure
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Apr
19
revised A condition that balls have finite measure
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Apr
19
comment A condition that balls have finite measure
The only "bad" case I could think of would be something like the completely discrete metric, $d(x,y) = 1$ for all $y \neq x$. It seems like many reasonable conditions could rule such things out, but I'm wondering what the most general could be....
Apr
19
comment A condition that balls have finite measure
@xavierm02: I could think of a discrete space, like the lattice of points in $\mathbb{R}^n$ with integer coordinates, where $\mu(A) = |A|$.
Apr
19
revised A condition that balls have finite measure
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Apr
19
asked A condition that balls have finite measure
Apr
19
revised Looking for a probability distribution in $\mathbb{R}^n$: exponentially decreasing density as distance from point
added 5 characters in body
Apr
19
revised Looking for a probability distribution in $\mathbb{R}^n$: exponentially decreasing density as distance from point
edited tags
Apr
19
accepted Quotation about usefulness of good definitions in maths?
Apr
19
revised Looking for a probability distribution in $\mathbb{R}^n$: exponentially decreasing density as distance from point
modified to L2 norm