A generalized strong law of large numbers

Strong laws of large numbers have been stated in the literature for measurable functions taking on values on different spaces. In this paper, a strong law of large numbers which generalizes some previous ones (like those for real-valued random variables and compact random sets) is established. This...

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Bibliographic Details
Published in:Probability theory and related fields 1999-06, Vol.114 (3), p.401-417
Main Authors: COLUBI, A, LOPEZ-DIAZ, M, SANTOS DOMINGUEZ-MENCHERO, J, ANGELES GIL, M
Format: Article
Language:English
Subjects:
Exact sciences and technology
Limit theorems
Mathematics
Metric space
Probability
Probability and statistics
Probability theory and stochastic processes
Random variables
Real variables
Sciences and techniques of general use
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Summary:Strong laws of large numbers have been stated in the literature for measurable functions taking on values on different spaces. In this paper, a strong law of large numbers which generalizes some previous ones (like those for real-valued random variables and compact random sets) is established. This law is an example of a strong law of large numbers for Borel measurable nonseparably valued elements of a metric space.
ISSN:0178-8051
1432-2064
DOI:10.1007/s004400050229