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April, 1986 An Inequality for the Hausdorff-Metric of $\sigma$-Fields
D. Landers, L. Rogge
Ann. Probab. 14(2): 724-730 (April, 1986). DOI: 10.1214/aop/1176992541


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.


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D. Landers. L. Rogge. "An Inequality for the Hausdorff-Metric of $\sigma$-Fields." Ann. Probab. 14 (2) 724 - 730, April, 1986.


Published: April, 1986
First available in Project Euclid: 19 April 2007

zbMATH: 0597.60003
MathSciNet: MR832034
Digital Object Identifier: 10.1214/aop/1176992541

Primary: 60A10
Secondary: 60G46

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

Rights: Copyright © 1986 Institute of Mathematical Statistics

Vol.14 • No. 2 • April, 1986
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