Approximation Theory in the Central Limit Theorem: Exact Results in Banach Spaces (Mathematics and its Applications, 32)

~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 Front Matter....Pages i-xviii General Questions of the Distribution Theory in Banach Spaces....Pages 1-10 Some Questions of Non-Linear Analysis....Pages 11-43 The Central Limit Theorem in Banach Spaces....Pages 44-61 Gaussian Measure of ε -Strip of Some Sets....Pages 62-79 Estimates of Rate of Convergence in the Central Limit Theorem....Pages 80-138 Back Matter....Pages 139-156