# usul

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 May7 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...! May7 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. May7 revised What exactly is a probability measure in simple words?added 208 characters in body May7 answered What exactly is a probability measure in simple words? Apr27 answered Ranked Preference Matching Algorithm Apr27 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! Apr27 awarded Critic Apr27 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. Apr21 revised A condition that balls have finite measureadded 2 characters in body Apr20 comment Looking for a probability distribution in $\mathbb{R}^n$: exponentially decreasing density as distance from pointThanks, 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! Apr20 revised A condition that balls have finite measuredeleted 15 characters in body Apr19 revised A condition that balls have finite measureadded 34 characters in body Apr19 comment A condition that balls have finite measureThe 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.... Apr19 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 $\mu(A) = |A|$. Apr19 revised A condition that balls have finite measureadded 2 characters in body Apr19 asked A condition that balls have finite measure Apr19 revised Looking for a probability distribution in $\mathbb{R}^n$: exponentially decreasing density as distance from pointadded 5 characters in body Apr19 revised Looking for a probability distribution in $\mathbb{R}^n$: exponentially decreasing density as distance from pointedited tags Apr19 accepted Quotation about usefulness of good definitions in maths? Apr19 revised Looking for a probability distribution in $\mathbb{R}^n$: exponentially decreasing density as distance from pointmodified to L2 norm