The Annals of Probability

An Inequality for the Hausdorff-Metric of $\sigma$-Fields

D. Landers and L. Rogge

Full-text: Open access

Abstract

It is shown that the Hausdorff-metric of $\sigma$-fields--which plays an important role for uniform martingale theorems--has a surprising "additivity" property. For example this property can be used to obtain a sharpened version of a uniform inequality for conditional expectations.

Article information

Source
Ann. Probab., Volume 14, Number 2 (1986), 724-730.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176992541

Digital Object Identifier
doi:10.1214/aop/1176992541

Mathematical Reviews number (MathSciNet)
MR832034

Zentralblatt MATH identifier
0597.60003

JSTOR
links.jstor.org

Subjects
Primary: 60A10: Probabilistic measure theory {For ergodic theory, see 28Dxx and 60Fxx}
Secondary: 60G46: Martingales and classical analysis

Keywords
Hausdorff-metric of $\sigma$-fields norm-inequalities for conditional expectations

Citation

Landers, D.; Rogge, L. An Inequality for the Hausdorff-Metric of $\sigma$-Fields. Ann. Probab. 14 (1986), no. 2, 724--730. doi:10.1214/aop/1176992541. https://projecteuclid.org/euclid.aop/1176992541


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