Ilya
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 1d comment Existence of a section of non-zero measure That's fine, it was just our of idle interest, and there was some progress on the problem. Perhaps, indeed I'll ask this on MO once I have time. 1d revised Lebesgue measure of closure of a set added 4 characters in body 1d answered Compactness of Set of Probability Measures 1d comment Intuition about Skorohod integral The latter integral sounds more like $\int_0^T W_1(t)\mathrm dW_2(t)$, since originally we have integrand being independent from the integrator, whereas in your latter integral they are the same. 1d comment Optimal point selection to maximize length of closest points interval ... let's say we have some equilibrium solution for $n - 2$, and $p_{n-2}$ is the lowest payoff, e.g. $p_2 = \frac12, p_3 = \frac14, p_4 = \frac16$. Then I make sure that boundary points for $n$ are $x_n$ and $1-x_n$ such that the rest of the players have no incentive to choose anything outside of $I_n := [x_n, 1-x_n]$, i.e. $p_{n-2}\cdot(1 - 2x_n) = x_n$. This way I find leftmost and rightmost points, and apply already known equilibrium to the remaining interval $I_n$. By no means I could prove yet the resulting strategy is always an equilibrium. 1d comment Optimal point selection to maximize length of closest points interval Agree with your solution. Also, to make easier all the $\varepsilon$ operations, I think we can focus on the space $I\times \{-, +\}$ so that there can be a choice of either side of a single point, with natural ordering of distances. It's a bit ugly, but at least seems to simplify some equilibrium strategies. For example, for $n = 2$ one equilibrium is $(\frac12-,\frac12+)$, for $n = 3$ it is $(\frac14, \frac12, \frac14)$, for $n = 4$ it is $(\frac16,\frac12-,\frac12+,\frac56)$. I think we can get all odd (even) cases from $n = 3$ ($n = 4$) by induction as follows:... 1d comment proving that fn is in the set of bounded real values on [0,1] with supremum metric It the function $f_n$ bounded? 1d comment “Set of observations” is an identity map - why such a framework? @MoebiusCorzer: never heard of it before, and there is no explicit link - at least based on what I just read about Stein's method. An interesting one, though - I also look into different kind of metrics, but on bigger spaces, so there may be some connections. 1d comment Infinite series contradiction Have you followed the link I've provided? All the definitions are there. 1d comment Infinite series contradiction No, it's a perfectly fine question to ask, but it is a bad thing to do. The reason is given in the link I've provided: if you rearrange the summands of not absolutely converging series, the sum changes. This does not happen to absolutely converging series. 1d revised Distribution with compact support added 13 characters in body 1d comment Distribution with compact support What is the space $D$? 1d comment “Set of observations” is an identity map - why such a framework? @MoebiusCorzer: section 2.1 here 2d comment Infinite series contradiction Terms rearrangement in series conditionally converging never should do you, young padawan. 2d comment “Set of observations” is an identity map - why such a framework? @MoebiusCorzer: I've found it interesting some time ago, and I have a couple of pages with rumblings on this topic, with examples if you are interested. 2d comment “Set of observations” is an identity map - why such a framework? @MoebiusCorzer: not sure I got you. To clarify, the random experiment on the range space $(E,\mathcal E)$ is the tuple $(\Omega, \mathcal F, \mathsf P, f)$ where $f$ is $\mathcal F|\mathcal E$-measurable. Then $\mathsf Q := \mathsf P\circ f^{-1}$ is the joint probability distribution. If you are given $(E,\mathcal E, \mathsf Q)$ you can construct a random experiment by taking $\Omega = E$, $\mathcal F = \mathcal E$, $\mathsf P = \mathsf Q$ - only $f$ is missing. It needs to satisfy $\mathsf P\circ f^{-1} = \mathsf P$, so $f = \mathrm{id}$ works. 2d comment If the 12% of a required number is $\sqrt{22+8\sqrt{16}} - \sqrt{22-8\sqrt{16}}$, what is the required number? Seems to be a direct way to solve this problem. You can also try the adjacent trick $\sqrt x - \sqrt y = \frac{x - y}{\sqrt x + \sqrt y}$, but I don't see any upside of using it here. 2d answered “Set of observations” is an identity map - why such a framework? 2d asked Optimal point selection to maximize length of closest points interval Nov 20 accepted Existence of a section of non-zero measure