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):
 LA6892MS
 DOE Contract Number:
 W7405ENG36
 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}
}
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