Approximation Theory in the Central Limit Theorem

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.