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\|	\|	almostsuremath.com Algebraic Probability - Almost Sure	7.3 parsecs away Travel
\|	\|	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...	7.3 parsecs away Travel
\|	\|	loureviews.blog LouReviews looks back at 2023: digital content - LouReviews	5.9 parsecs away Travel
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\|	\|	mkatkov.wordpress.com On the density estimation \| Crackpot Trisector Notes	7.3 parsecs away Travel
\|	\|	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...	7.3 parsecs away Travel
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