Ergodic theorem for random measures, homogeneous in a broad sense
type: Item
instance of: scholarly article
title: Ergodic theorem for random measures, homogeneous in a broad sense
zbMATH Open document ID: 0575.60053
DOI: 10.1007/BF00970329
author: Eh. Garonas
published in: Lithuanian Mathematical Journal
publication date: 1984-01-01T00:00:00Z
review text: Suppose \(\mu\) is a second order stationary random measure on \({\mathbb{R}}^ d\), and let m denote d-dimensional Lebesgue measure. The ergodic theorem proved asserts that \(m(B_ n)^{-1}\mu (B_ n)\) converges in mean square for a class of directed nets of Borel subsets \(B_ n\) of \({\mathbb{R}}^ d\), called in this paper \(\alpha\)-ergodic nets.
Mathematics Subject Classification ID: 60G57
Mathematics Subject Classification ID: 60F25
Mathematics Subject Classification ID: 60G10
zbMATH DE Number: 3919474
zbMATH Keywords: stationary random measure
zbMATH Keywords: ergodic theorem
zbMATH Keywords: directed nets of Borel subsets
Wikidata QID: Q112879214
reviewed by: F. Papangelou
MaRDI profile type: Publication
cites work: Q3252160
cites work: Ergodic theorems for superadditive processes.
cites work: Q5652029
cites work: Ergodic theorems for subadditive spatial processes
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cites work: Q5845326
cites work: The ergodic theorem
full work available at URL: https://doi.org/10.1007/bf00970329
OpenAlex ID: W2093777080
description: scientific article; zbMATH DE number 3919474