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Title: Purely set theoretic foundation for measure theory with an application to hierarchical inference

Abstract

A simple set of axioms is given for a class of subsets of an abstract set, Z, called ''intervals'', and an assigned ''measure'' for intervals, from which the basic theorems of measure theory are derived. Such a nontopological formulation is required in introducing a measure in a set of graphs, and was developed earlier for that purpose in a more complicated way. The theory is shown to apply to the set of all state vectors of an infinite hierarchical inference tree. 1 figure.

Authors:
;
Publication Date:
Research Org.:
Los Alamos Scientific Lab., N.Mex. (USA)
OSTI Identifier:
7211558
Report Number(s):
LA-6892-MS
DOE Contract Number:
W-7405-ENG-36
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; MEASURE THEORY; MATHEMATICAL LOGIC; MATHEMATICS; 990200* - Mathematics & Computers

Citation Formats

Everett, C.J., and Cashwell, E.D. Purely set theoretic foundation for measure theory with an application to hierarchical inference. United States: N. p., 1977. Web.
Everett, C.J., & Cashwell, E.D. Purely set theoretic foundation for measure theory with an application to hierarchical inference. United States.
Everett, C.J., and Cashwell, E.D. Fri . "Purely set theoretic foundation for measure theory with an application to hierarchical inference". United States. doi:.
@article{osti_7211558,
title = {Purely set theoretic foundation for measure theory with an application to hierarchical inference},
author = {Everett, C.J. and Cashwell, E.D.},
abstractNote = {A simple set of axioms is given for a class of subsets of an abstract set, Z, called ''intervals'', and an assigned ''measure'' for intervals, from which the basic theorems of measure theory are derived. Such a nontopological formulation is required in introducing a measure in a set of graphs, and was developed earlier for that purpose in a more complicated way. The theory is shown to apply to the set of all state vectors of an infinite hierarchical inference tree. 1 figure.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Fri Jul 01 00:00:00 EDT 1977},
month = {Fri Jul 01 00:00:00 EDT 1977}
}

Technical Report:
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