File:Measurable Factorization.svg
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Captions
Captions
Commutative diagram (mathematics) for the factorization lemma in measure theory.
Summary[edit]
| Description |
English: In measure theory (mathematics), the factorization lemma charaterizes all those functions g, which are measurable with respect to a sigma-algebra sigma(f), induced on the origin space X1 by another function f. It says, that g is measurable w.r.t. the f-induced sigma-algebra sigma(f), if and only if g factorizes through f as a composition of measurable mappings. |
| Date | |
| Source | Own work |
| Author | EinMathematikerInAustria |
Generated with latex, pdfcrop and an online pdf-to-svg converter as described in https://meta.wikimedia.org/wiki/Help:Displaying_a_formula#Commutative_diagrams
LaTeX-Code:
\documentclass{amsart} \usepackage{amsmath,amssymb,nopageno} \usepackage[all]{xy} \DeclareMathOperator{\Ker}{ker} \begin{document}
\begin{equation*}
\xymatrix@C+1em@R+1em{
(X_1,\sigma(f)) \ar[r]^-{g} \ar[d]_-{f} & (X_3,\mathcal{A}_3) \\
(X_2,\mathcal{A}_2) \ar@{-->}[ur]_-{\tilde{g}}
}
\end{equation*}
\end{document}
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This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
| The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 09:30, 17 February 2024 | | 151 × 84 (10 KB) | EinMathematikerInAustria (talk | contribs) | Uploaded own work with UploadWizard |
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