Questions tagged [pushforward]

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36 questions
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Why is it necessary to talk about a pushforward measure?

I understand that a random variable $X$ and a probability measure $P$ on a space $(\Omega,\mathcal{A})$ induce the distribution $P_X$ on a space $(\Omega',\mathcal{A}')$. But is there an example ...
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Pushforward formula for Lebesgue Stieltjes Measure

I got to have this problem in my hand. Problem Let $F: \mathbb{R}\rightarrow \mathbb{R}$ be an increasing, right continuous function, and let $\phi :\mathbb{R}\rightarrow \mathbb{R}$ be a ...
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Finding the components of a pushforward vector in local coordinates

Let $\phi:M\rightarrow N$ be a smooth map between smooth manifolds, $v \in \operatorname{Vect}(M)$. Let $\{x^\mu\}$ and $\{y^i\}$ be local coordinates on $M$ and $N$ respectively. How can I show that ...
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Operation on Vector fields

I am analyzing a program which transforms vector fields by action of diffeomorphisms and feedbacks. Here are the operation that I don't understand (it's Mathematica code) ...
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I'm having some problems in showing that, given a probability measure $\mu$ on $\mathbb{R}^d$, if $s,t:\mathbb{R}^d\to\mathbb{R}^d$ are such that $(\textrm{id}\times s)_\#\mu=(\textrm{id}\times t)_\#\... 0answers 82 views Push-forward and Category theory There obviously seems to be a connection between the push-forward and the pull-back of a smooth function$f:M \to N$between smooth manifolds, and the Hom-maps from category theory$f^*=Mor_C(f,\...
Trying to prove $df_{F(p)}(F_*(v_p)) = F^*(df_{F(p)})(v_p)$. It is given that F is a smooth function between manifolds M and N, p $\in$ M, $v_p \in T_pM$ and $df_{F(p)} \in T_{F(p)}^*N$.