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fabricebaudoin.blog | ||
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pfzhang.wordpress.com
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| | | | | Consider a smooth one-parameter family $latex {f_t}$ of diffeomorphisms on a manifold $latex M$. It is a flow if $latex f_0(x)=x$ and $latex f_{t}\circ f_{s}(x) = f_{s+t}(x)$ for every $latex x\in M$, , $latex t ,s \in \mathbb{R}$. Set $latex X(x)=\lim\limits_{h\to 0} \frac{1}{h}(f_h(x) - x)$. This generates a vector field $latex X: M \to TM$.... | |
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almostsuremath.com
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| | | | | The aim of this post is to motivate the idea of representing probability spaces as states on a commutative algebra. We will consider how this abstract construction relates directly to classical probabilities. In the standard axiomatization of probability theory, due to Kolmogorov, the central construct is a probability space $latex {(\Omega,\mathcal F,{\mathbb P})}&fg=000000$. This consists... | |
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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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badarchaeology.wordpress.com
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| | | Microletters reading REX JESVS | ||
