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Results tagged with convex-analysis
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user 4832
7
votes
Accepted
Convex function and weak convergence of measures
Let $\mathscr{X}$ be a locally convex space and $X \subset \mathscr{X}$ compact.
Let $E = \{f \in C(X) : \langle f, \mu_n \rangle \to \langle f, \mu \rangle\}$. It's easy to see that $E$ is a closed …
- 29.8k
4
votes
Question on Jensen's inequality
Let $Z_1, Z_2$ be two independent fair coin flips, i.e. $P(Z_i = 1) = P(Z_i = -1) = 1/2$. Let $X = 2 Z_1$ and $Y = X + 1_{\{Z_1 = -1\}} Z_2$. Then $(X,Y)$ is a martingale. In words, a gambler bets …
- 29.8k
12
votes
Accepted
Constructing an independent uniform random variable from two independent ones
I think this works for a continuous $h$.
Let $f : \mathbb{R} \to [0,1]$ be the "triangle wave" function given on $[0,1]$ by
$$f(u) = \begin{cases}1-2u, & 0 \le u \le \frac{1}{2} \\ 2u-1, & \frac{1}{2 …
- 29.8k