Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-22T20:50:53.251Z Has data issue: false hasContentIssue false

Martingale convergence theorems for sequences of Stone algebras

Published online by Cambridge University Press:  18 May 2009

J. D. Maitland Wright
Affiliation:
St. Catherine's College, Oxford
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A vector lattice W is boundedly complete when each subset {aj:j ∊ J} of W which is bounded above by an element of W has a least upper bound in W. The least upper bound of {aj:j ∊ J} is denoted by and the greatest lower bound by whenever these exist.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 1969

References

REFERENCES

1.Andersen, E. Sparre and Jessen, B., Some limit theorems on set functions, Mat.-Fys. Medd. Danske Vid. Selsk. 25 (1948), No. 5.Google Scholar
2.Doob, J. L., Stochastic processes (Wiley, New York, 1953).Google Scholar
3.Floyd, E. E., Boolean algebras with pathological order topologies, Pacific J. Math. 5 (1955), 687689.CrossRefGoogle Scholar
4.Stone, M. H., Boundedness properties in function lattices, Canad. J. Math. 1 (1949), 176186.CrossRefGoogle Scholar
5.Wright, J. D. Maitland, Stone algebra valued measures and integrals, Proc. London Math. Soc.; to appearGoogle Scholar
6.Wright, J. D. Maitland, A Radon-Nikodym theorem for Stone algebra valued measures, Trans. Amer. Math. Soc; to appear.Google Scholar
7.Wright, J. D. Maitland, Applications to averaging operators of the theory of Stone algebra valued measure, Quart. J. Math. Oxford Ser. (2) 19 (1968), 321331.CrossRefGoogle Scholar