Abstract
A salient underpinning of probability theory is the one-to-one correspondence between distribution functions onR nand probability measures on the Borel subsets ofR n. Verification of this correspondence involves the notion of measure extension.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
J. L. DoobStochastic ProcessesWiley, New York, 1953.
P. R. HalmosMeasure TheoryVan Nostrand, Princeton, 1950; Springer-Verlag, Berlin and New York, 1974.
G. H. Hardy, J. E. Littlewood, and G. PolyaInequalitiesCambridge Univ. Press, London, 1934.
A. N. Kolmogorov, Foundations of Probability (Nathan Morrison, translator), Chelsea, New York, 1950.
M. LoèveProbability Theory3rd ed., Van Nostrand, Princeton, 1963; 4th ed., Springer-Verlag, Berlin and New York, 1977–1978.
E. J. McShaneIntegrationPrinceton Univ. Press, Princeton, 1944.
M. E. MonroeIntroduction to Measure and IntegrationAddison—Wesley, Cambridge, Mass., 1953.
H. Robbins, “Mixture of Distributions,” Ann.Math. Statist. 19(1948), 360–369.
S. SaksTheory of the Integral(L. C. Young, translator), Stechert—Hafner, New York, 1937.
J. L. Snell, “Applications of martingale system theorems,”Trans. Amer. Math. Soc.73 (1952), 293–312.
D. V. WidderAdvanced Calculus2nd ed., Prentice—Hall, Englewood Cliffs, New Jersey, 1961.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media New York
About this chapter
Cite this chapter
Chow, Y.S., Teicher, H. (1997). Measure Extensions, Lebesgue—Stieltjes Measure, Kolmogorov Consistency Theorem. In: Probability Theory. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1950-7_6
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1950-7_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-40607-7
Online ISBN: 978-1-4612-1950-7
eBook Packages: Springer Book Archive