(MEASURE THEORY - Storming Media

REPRESENTING FINITELY ADDITIVE INVARIANT PROBABILITIES.

15 MAR 1968

1 pages

Authors: Richard A. Olshen; STANFORD UNIV CALIF DEPT OF STATISTICS

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Hewitt and Savage have shown that finitely additive exchangeable probabilities on a product space are integral averages of power product probabilities. They prove this result as a corollary to their theorems on the countably additive case. This note adapts their technique to the study of more general invariant probabilities. From results of Farrell and Choquet and Feldman it is concluded that finitely additive invariant probabilities are averages of finitely additive ...

ERGODIC THEORY AND DISCRETE TRANSPORT PROCESSES.

OCT 1967

Authors: H. Hejtmanek; ATOMINSTITUT DER OESTERREICHISCHEN HOCHSCHULEN VIENNA

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Discrete transport processes occur in the computational treatment of neutron transport problems in reactor physics and shielding. The time dependance of the particle density function, especially the asymptotic behavior of it, has been studied. Mean ergodic theory is applied to prove uniqueness of equilibrium. Then mixing and ergodicity of the transport process is established. (Author)

CLASSICAL TRANSFORMS OF MEASURES AND L(1) FUNCTIONS,

OCT 1965

Authors: John J. Benedetto; MARYLAND UNIV COLLEGE PARK INST FOR FLUID DYNAMICS AND APPLIED MATHEMATICS

NOTES ON SPECTRAL THEORY.

DEC 1964

Authors: C. Ionescu Tulcea; ILLINOIS UNIV URBANA DEPT OF MATHEMATICS

The report contains definitions and results concerning semi-spectral and spectral families of Radon measures. Topics covered include: (a) Semi-spectral and spectral families of Radon measures; (b) Remarks on scalar operators; (c) Abstract valued measures associated with operators; (d) Scalar dilations and scalar extensions of operators on Banach spaces; and (e) Conditions implying that a subscalar operator is scalar.

USE OF TRANSFORMATIONS ON PARAMETERS IN NON-LINEAR THEORY. II. MEASURES OF NONLINEARITY AND TRANSFORMATIONS TO REDUCE NON-LINEARITY,

JUL 1964

Authors: Irwin Guttman; Duane A. meeter; WISCONSIN UNIV MADISON DEPT OF STATISTICS

Non-linear least squares problems, and measures of non-linearity are discussed. Some measures of nonlinearity due to Beale (1960 are introduced), and the behavior of these measures is examined using certain specific examples. The effect of using transformations of parameters to reduce the non-linearity measures is investigated.

AN ' 'ALTERNIERENDE VERFAHREN' ' FOR GENERAL POSITIVE OPERATORS,

1962

Authors: Gian-Carlo Rota; MASSACHUSETTS INST OF TECH CAMBRIDGE

Notes on Measure Theory. Part I. Lattices and Lattice Functionals.

01 AUG 1951

Authors: B. J. Pettis; TULANE UNIV NEW ORLEANS LA

These notes represent an introduction to measure theory from the viewpoint of lattices and lattice functionals. The viewpoint followed here is not at all new; it goes back at least as far as a paper by Caratheodory in 1938, and was advanced considerably in the original (1940) edition of Garrett Birkhoff's Lattice Theory. The material is simply an abstraction of that part of point set theory usually described as measure ...