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Linear Approximations in Convex Metric Spaces

By: Bela Gyires

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Hardcover | 1 December 1992

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Hardcover
140 Pages

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22.86 x 16.51 x 1.27

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The average of a family of probability distribution functions (in short, distribution function) by a distribution function, as weight function, is also a distribution function. This average is said to be the mixture of the family of distribution functions by the weight function. What are the conditions for the existence of a weight function? If such a weight function exists, what is that function? These problems are said to be the problems of linear approximability, or decomposability for distribution functions. Questions concerning this topic have been raised long ago. Only "ad hoc" procedures have been found. General methods for these problems have not been worked out. In this book, the author deals with the treatment of such general method.

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Non-Fiction Mathematics Topology Geometry Probability & Statistics Applied Mathematics Engineering & Technology Mechanical Engineering & Materials Materials Science Computing & I.T.Computer Science Booktopia Publisher Services

World Scientific Publishing

Introduction	p. 1
Linear approximation in convex metric spaces	p. 5
Convex metric spaces	p. 5
Convex spaces	p. 6
Convex metric spaces	p. 8
Decomposability in totally convex metric spaces	p. 14
Integration in totally convex metric spaces	p. 14
Decomposability of elements of a totally convex metric space	p. 16
Special cases	p. 20
The set of weight functions is the set of discrete probability distribution functions with jumps at finitely many prescribed points	p. 20
The set of weight functions is the set of discrete probability distribution functions with jumps at infinitely many prescribed points	p. 23
The set of weight functions is the set of absolutely continuous probability distribution functions with square integrable density function	p. 29
Decomposability of distribution functions	p. 35
Formulation of the problem	p. 35
Decomposability of distribution functions	p. 49
Considerations on the set of all probability distribution functions	p. 50
Considerations on the set of probability distribution functions concentrated on a finite or infinite interval	p. 63
Considerations on the set of continuous probability distribution functions	p. 70
Considerations on the set of discrete probability distribution functions	p. 84
App. A Two theorems on mixtures of probability distribution functions	p. 97
App. B Totally positive matrices. The transsignation of a matrix	p. 100
App. C The determinant theorem of Cauchy, with corollaries	p. 101
App. D A representation of two polynomials	p. 105
App. E Cauchy matrices of special type	p. 107
App. F On a matrix identity	p. 110
App. G Solution of a matrix equation. On an extension of the Sherman-Morrison theorem	p. 112
App. H The moment problem of Hamburger. On the solution of the full moment problem of Stieltjes	p. 116
App. J Integration by parts for Stieltjes integrals	p. 123
References and bibliography	p. 129
Index	p. 132
Table of Contents provided by Blackwell. All Rights Reserved.

Linear Approximations in Convex Metric Spaces

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