Approximation Theory in the Central Limit Theorem

Inhaltsverzeichnis

• 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.