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I was trying to understand stochastic dominance when I came across this problem (Question 2). How do I show that the set of probability distributions that first/second-order stochastically dominate $p$ is closed and convex?

I have attempted to solve the set of FOSD is convex; but how do I show that the "limit" of probability distributions is also in the set (i.e. the set is closed)?

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  • $\begingroup$ Please make your question selfcontained. $\endgroup$ Commented Oct 12, 2023 at 22:19

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