# 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}

}

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