Probability Theory I

1. Front Matter

   Pages i-xvii

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2. Elementary Probability Theory

   1. Elementary Probability Theory

      • M. Loève

      Pages 1-52

3. Notions of Measure Theory

   1. Front Matter

      Pages 53-53

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   2. Sets, Spaces, and Measures

      • M. Loève

      Pages 55-102

   3. Measurable Functions and Integration

      • M. Loève

      Pages 103-147

4. General Concepts and Tools of Probability Theory

   1. Front Matter

      Pages 149-149

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   2. Probability Concepts

      • M. Loève

      Pages 151-176

   3. Distribution Functions and Characteristic Functions

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      Pages 177-232

5. Independence

   1. Front Matter

      Pages 233-233

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   2. Sums of Independent Random Variables

      • M. Loève

      Pages 235-279

   3. Central Limit Problem

      • M. Loève

      Pages 280-352

   4. Independent Identically Distributed Summands

      • M. Loève

      Pages 353-405

6. Back Matter

   Pages 407-428

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This fourth edition contains several additions. The main ones con­ cern three closely related topics: Brownian motion, functional limit distributions, and random walks. Besides the power and ingenuity of their methods and the depth and beauty of their results, their importance is fast growing in Analysis as well as in theoretical and applied Proba­ bility. These additions increased the book to an unwieldy size and it had to be split into two volumes. About half of the first volume is devoted to an elementary introduc­ tion, then to mathematical foundations and basic probability concepts and tools. The second half is devoted to a detailed study of Independ­ ence which played and continues to playa central role both by itself and as a catalyst. The main additions consist of a section on convergence of probabilities on metric spaces and a chapter whose first section on domains of attrac­ tion completes the study of the Central limit problem, while the second one is devoted to random walks. About a third of the second volume is devoted to conditioning and properties of sequences of various types of dependence. The other two thirds are devoted to random functions; the last Part on Elements of random analysis is more sophisticated. The main addition consists of a chapter on Brownian motion and limit distributions.

• Median
• Probability
• Probability distribution
• Probability space
• Probability theory
• Random variable
• Variance
• Wahrscheinlichkeitsrechnung
• measure theory

• Departments of Mathematics and Statistics, University of California at Berkeley, Berkeley, USA

  M. Loève

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