Distances in Probability Theory

Michel Marie Deza and Elena Deza
Additional contact information
Michel Marie Deza: Ecole Normale Supérieure
Elena Deza: Moscow State Pedagogical University

Chapter Chapter 14 in Encyclopedia of Distances, 2016, pp 259-274 from Springer

Abstract: Abstract A probability space is a measurable space $$(\varOmega,\mathcal{A},P)$$ , where $$\mathcal{A}$$ is the set of all measurable subsets of Ω, and P is a measure on $$\mathcal{A}$$ with P(Ω) = 1. The set Ω is called a sample space. An element $$a \in \mathcal{A}$$ is called an event. P(a) is called the probability of the event a. The measure P on $$\mathcal{A}$$ is called a probability measure, or (probability) distribution law, or simply (probability) distribution.

Keywords: Transportation Distance; Absolute Moment; Bregman Divergence; Nondecreasing Continuous Function; Leibler Distance (search for similar items in EconPapers)
Date: 2016
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-52844-0_14

Ordering information: This item can be ordered from
http://www.springer.com/9783662528440

DOI: 10.1007/978-3-662-52844-0_14

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().