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wildtopology.com | ||
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djalil.chafai.net
Today, part of my teaching concerned basic properties of the total variation on discrete spaces. Let \( {E} \) be a possibly infinite countable set equipped with its discrete topology and \( {\sigma} \)-field. Let \( {\mathcal{P}} \) be the set of probability measures on \( {E} \). We equip \( {\mathcal{P}} \) with the total variation distance defined for... |
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dominiczypen.wordpress.com
The starting point of this blog post is a slight reformulation of the $latex T_0$ separation axiom: A topological space $latex (X,\tau)$ is $latex T_0$ if for all $latex x\neq y\in X$ there is a set $latex U\in \tau$ such that $latex \{x,y\}\cap U \neq \emptyset \text{ and } \{x,y\}\not\subseteq U.$ Given a cardinal $latex... |
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fabricebaudoin.blog
Exercise 1.Solve Exercise 44 in Chapter 1 of the book. Exercise 2.Solve Exercise 3 in Chapter 1 of the book. Exercise 3.Solve Exercise 39 in Chapter 1 of the book. Exercise 4.The heat kernel on $latex \mathbb{S}^1$ is given by $latex p(t,y) =\frac{1}{2\pi}\sum_{m \in \mathbb{Z}} e^{-m^2 t} e^{im y} =\frac{1}{\sqrt{4\pi t}} \sum_{k \in \mathbb{Z}} e^{-\frac{(y... |
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www.piotrgryko.com
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