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tEL moi, .. ,' si favait su comment en revenir. je One service mathematics has rendered the n 'y serais point alle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled' discarded nonsense'. The series is divergent; therefore we may be Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought A highly necessary tool in a world where both feedback and nonlineari ties abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sci ences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One ser vice topology has rendered mathematical physics .. .'; 'One service logic has rendered computer 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.

Strong Limit Theorems

Introduction. 1. Preliminaries. 1. Stationary Sequence (Mixing Conditions, Basic Inqualities). 2. Wiener Process (increment Theory). 3. Skorokhod Theorem. 4. Martingale Convergence Theorem and Goal-Koksme Strong Law of Large Numbers. 5. Moricz Exponent Inequality.2. I.I.D.R.V. 1. Strassen Strong Invariance Principle. 2. Improvement of the Rate of Convergence. 3. The Best Rate, K-M-T Theorem. 4. Increments of Partial Sums. 3. Independent Non-Identically Distributed R.V. 1. Strong Approximations of Partial Sums by Wiener Process. 2. Increments of Partial Sums. 4. Stationary Sequence. 1. Basic Method and its Improvement. 2. Strong Approximations of (alphabeta-Mixing Sequence. 3. Mixing Rate and Approximation Remainder Term. 4. Strong Approximations of alpha(pi)-Mixing Sequence. 5. Strong Approximations of Functions of Mixing Sequence. 6. Increments of Partial Sums for phi-Mixing Sequence. 5. Strong Approximations of Other Kinds of Dependent Sequence and Statistics. 1. Lacunary Trigonometric Series. 2. Gaussian Sequence. 3. Additive Functional of Markov Process. 4. U-Statistics. 5. Estimators of Error Variance. 6. Miscellany.