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Linear Approximations in Convex Metric Spaces - Bela Gyires

Linear Approximations in Convex Metric Spaces

Hardcover Published: 1993
ISBN: 9789810214838
Number Of Pages: 140

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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.

Introductionp. 1
Linear approximation in convex metric spacesp. 5
Convex metric spacesp. 5
Convex spacesp. 6
Convex metric spacesp. 8
Decomposability in totally convex metric spacesp. 14
Integration in totally convex metric spacesp. 14
Decomposability of elements of a totally convex metric spacep. 16
Special casesp. 20
The set of weight functions is the set of discrete probability distribution functions with jumps at finitely many prescribed pointsp. 20
The set of weight functions is the set of discrete probability distribution functions with jumps at infinitely many prescribed pointsp. 23
The set of weight functions is the set of absolutely continuous probability distribution functions with square integrable density functionp. 29
Decomposability of distribution functionsp. 35
Formulation of the problemp. 35
Decomposability of distribution functionsp. 49
Considerations on the set of all probability distribution functionsp. 50
Considerations on the set of probability distribution functions concentrated on a finite or infinite intervalp. 63
Considerations on the set of continuous probability distribution functionsp. 70
Considerations on the set of discrete probability distribution functionsp. 84
App. A Two theorems on mixtures of probability distribution functionsp. 97
App. B Totally positive matrices. The transsignation of a matrixp. 100
App. C The determinant theorem of Cauchy, with corollariesp. 101
App. D A representation of two polynomialsp. 105
App. E Cauchy matrices of special typep. 107
App. F On a matrix identityp. 110
App. G Solution of a matrix equation. On an extension of the Sherman-Morrison theoremp. 112
App. H The moment problem of Hamburger. On the solution of the full moment problem of Stieltjesp. 116
App. J Integration by parts for Stieltjes integralsp. 123
References and bibliographyp. 129
Indexp. 132
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9789810214838
ISBN-10: 9810214839
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 140
Published: 1993
Publisher: World Scientific Publishing Co Pte Ltd
Country of Publication: SG
Dimensions (cm): 22.86 x 16.51  x 1.27
Weight (kg): 0.32

Earn 282 Qantas Points
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