Illinois Journal of Mathematics

Infinite products of infinite measures

Peter A. Loeb and David A. Ross

Full-text: Open access

Abstract

Let $(X_i,{\mathscr B}_i,m_i)$ $(i\in{\mathbb N})$ be a sequence of regular Borel measure spaces. There is a Borel measure $\mu$ on $\prod_{i\in{\mathbb N}}{X_i}$ such that if $K_i\subseteq X_i$ is compact for all $i\in{\mathbb N}$ and $\prod_{i\in{\mathbb N}}{m_i(K_i)}$ converges, then $\mu({\prod_{i\in{\mathbb N}}{K_i}})=\prod_{i\in{\mathbb N}}{m_i(K_i)}$.

Article information

Source
Illinois J. Math., Volume 49, Number 1 (2005), 153-158.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138311

Digital Object Identifier
doi:10.1215/ijm/1258138311

Mathematical Reviews number (MathSciNet)
MR2157373

Zentralblatt MATH identifier
1083.28003

Subjects
Primary: 28A35: Measures and integrals in product spaces
Secondary: 28A12: Contents, measures, outer measures, capacities 28E05: Nonstandard measure theory [See also 03H05, 26E35]

Citation

Loeb, Peter A.; Ross, David A. Infinite products of infinite measures. Illinois J. Math. 49 (2005), no. 1, 153--158. doi:10.1215/ijm/1258138311. https://projecteuclid.org/euclid.ijm/1258138311


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