Approximation Theory in the Central Limit Theorem
Exact Results in Banach Spaces
Published in July 1989
Book
Hardback
XVIII, 176 pages
978-90-277-2825-8 (ISBN)
Description
~Et mai ..., si j'avait su comment en revenir. One service mathematics has rendered the human race. It has put common sense back je n'y serais point aIIe.' Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent: therefore we may be sense' . able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ...'; 'One service logic has rendered com- puter science ...'; 'One service category theory has rendered mathematics ...'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
More details
Series
Language
English
Place of publication
Dordrecht
Netherlands
Publishing group
Springer
Target group
College/higher education
Professional and scholarly
Illustrations
biography
Dimensions
Height: 250 mm
Weight
500 gr
ISBN-13
978-90-277-2825-8 (9789027728258)
DOI
10.1007/978-94-011-7798-6
Schweitzer Classification
Other editions
Additional editions
V. Paulauskas | A. Rackauskas
Approximation Theory in the Central Limit Theorem
Exact Results in Banach Spaces
Book
04/2012
Springer
€53.49
Shipment within 15-20 days
Content
1. General Questions of the Distribution Theory in Banach Spaces.- 1.1. Random Elements in Banach Spaces.- 1.2. Main Facts on Gaussian Measures in Banach Spaces.- 1.3. Weak Convergence of Probability Measures and Some Inequalities.- 2. Some Questions of Non-Linear Analysis.- 2.1. Differentiation in Normed Spaces.- 2.2. Smooth Approximation in a Banach Space.- 2.3. Supplements.- 3. The Central Limit Theorem in Banach Spaces.- 3.1. Operators of Type p.- 3.2. The Central Limit Theorem.- 3.3. Supplements.- 4. Gaussian Measure of ?-Strip of Some Sets.- 4.1. General Remarks.- 4.2. Distribution Density of the Norm of a Gaussian Element in Lp.- 4.3. Distribution Density of the Norm of a Gaussian Element in c0.- 4.4. Supplements.- 5. Estimates of Rate of Convergence in the Central Limit Theorem.- 5.1. Estimates of the Rate of Convergence on Sets.- 5.2. Estimates of the Rate of Convergence in the Central Limit Theorem in Some Banach Spaces.- 5.3. Estimates of the Rate of Convergence in the Prokhorov Metric and the Bounded Lipschitz Metric.- 5.4. Supplements.- Bibliographical Notes.- References.