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xorshammer.com | ||
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richardzach.org
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| | | | | Baaz, Matthias, and Richard Zach. 2022. Epsilon theorems in intermediate logics. The Journal of Symbolic Logic 87(2), pp. 682-720. DOI: 10.1017/jsl.2021.103. Open access. Any intermediate propositi... | |
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almostsuremath.com
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| | | | | I start these notes on stochastic calculus with the definition of a continuous time stochastic process. Very simply, a stochastic process is a collection of random variables $latex {\{X_t\}_{t\ge 0}}&fg=000000$ defined on a probability space $latex {(\Omega,\mathcal{F},{\mathbb P})}&fg=000000$. That is, for each time $latex {t\ge 0}&fg=000000$, $latex {\omega\mapsto X_t(\omega)}&fg=000000$ is a measurable function from $latex... | |
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homotopytypetheory.org
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| | | | | Thierry Coquand and I have proved that, for a large class of algebraic structures, isomorphism implies equality (assuming univalence). A class of algebraic structures Structures in this class consist of a type, some operations on this type, and propositional axioms that can refer to operations and other axioms. N-ary functions are defined in the following... | |
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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... | ||
