## The Annals of Probability

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

#### 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

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
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