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fabricebaudoin.blog | ||
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mikespivey.wordpress.com
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| | | | | The Riemann zeta function $latex \zeta(s)$ can be expressed as $latex \zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^s}$, for complex numbers s whose real part is greater than 1. By analytic continuation, $latex \zeta(s)$ can be extended to all complex numbers except where $latex s = 1$. The power sum $latex S_a(M)$ is given by $latex S_a(M) =... | |
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mkatkov.wordpress.com
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| | | | | For probability space $latex (\Omega, \mathcal{F}, \mathbb{P})$ with $latex A \in \mathcal{F}$ the indicator random variable $latex {\bf 1}_A : \Omega \rightarrow \mathbb{R} = \left\{ \begin{array}{cc} 1, & \omega \in A \\ 0, & \omega \notin A \end{array} \right.$ Than expected value of the indicator variable is the probability of the event $latex \omega \in... | |
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jmanton.wordpress.com
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| | | | | If $latex Y$ is a $latex \sigma(X)$-measurable random variable then there exists a Borel-measurable function $latex f \colon \mathbb{R} \rightarrow \mathbb{R}$ such that $latex Y = f(X)$. The standard proof of this fact leaves several questions unanswered. This note explains what goes wrong when attempting a "direct" proof. It also explains how the standard proof... | |
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isaacslavitt.com
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