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2024 | OriginalPaper | Chapter

On Disintegration of Measures in Optimal Transport

Author : Hung T. Nguyen

Published in: Applications of Optimal Transport to Economics and Related Topics

Publisher: Springer Nature Switzerland

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Abstract

As part of a prelude to the applications of optimal transport theory to econometrics and machine learning, this tutorial paper focus on the notion of disintegration in measure theory in the analysis of Wassersrein metrics which are useful, in particular, for machine learning and financial risks. An elementary exposition on using disintegration to prove that Waserstein divergence is a bona fide metric is provided.

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previous chapter Forecasting GDP with Many Predictors Using Sparse-Group LASSO MIDAS
next chapter Why Micro-funding? Why Small Businesses Are Important? Analysis Based on First Principles
Literature
1.
Dudley, R.M.: Real Analysis and Probability. Cambridge University Press (2003)
2.
Galichon, A.: Optimal Transport Methods in Economics. Princeton University Press (2016)
3.
Graf, S., Mauldin, R.D.: A Classification of Disintegration of Measures, in Measure and Measurable Dynamics, No. 94, pp. 147–158. Contemp. Math, AMS (1989)
4.
Villani, C.: Topics in Optimal Transportation. AMS (2003)
5.
Villani, C.: Optimal Transport: Old and New. Springer (2009)
Metadata
Title
On Disintegration of Measures in Optimal Transport
Author
Hung T. Nguyen
Copyright Year
2024
Book
Applications of Optimal Transport to Economics and Related Topics

Print ISBN: 978-3-031-67769-4

Electronic ISBN: 978-3-031-67770-0

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-3-031-67770-0_11

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