# 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}

}

Other availability

Please see Document Availability for additional information on obtaining the full-text document. Library patrons may search WorldCat to identify libraries that may hold this item. Keep in mind that many technical reports are not cataloged in WorldCat.

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.