دوره‌ای در نظریه احتمال (ویرایش بازنگری‌شده)

Since the publication of the first edition of this classic textbook over thirty years ago, tens of thousands of students have used A Course in Probability Theory . New in this edition is an introduction to measure theory that expands the market, as this treatment is more consistent with current courses. While there are several books on probability, Chung's book is considered a classic, original work in probability theory due to its elite level of sophistication. Cover......Page 1 Course in Probability Theory......Page 3 Copyright......Page 4 Contents......Page 5 Preface to the third edition......Page 8 Preface to the second edition......Page 10 Preface to the first edition......Page 12 1 Distribution function......Page 16 2.1 Classes of sets......Page 30 2.2 Probability measures and their distribution functions......Page 35 3.1 General definitions......Page 48 3.2 Properties of mathematical expectation......Page 55 3.3 Independence......Page 67 4.1 Various modes of convergence......Page 82 4.2 Almost sure convergence; Borel-Cantelli lemma......Page 89 4.3 Vague convergence......Page 98 4.4 Continuation......Page 105 4.5 Uniform integrability; convergence of moments......Page 113 5.1 Simple limit theorems......Page 120 5.2 Weak law of large numbers......Page 126 5.3 Convergence of series......Page 135 5.4 Strong law of large numbers......Page 143 5.5 Applications......Page 152 6.1 General properties; convolutions......Page 164 6.2 Uniqueness and inversion......Page 174 6.3 Convergence theorems......Page 183 6.4 Simple applications......Page 189 6.5 Representation theorems......Page 201 6.6 Multidimensional case ; Laplace transforms......Page 210 7.1 Liapounov's theorem......Page 219 7.2 Lindeberg-Feller theorem......Page 228 7.3 Ramifications of the central limit theorem......Page 238 7.4 Error estimation......Page 249 7.5 Law of the iterated logarithm......Page 256 7.6 Infinite divisibility......Page 264 8.1 Zero-or-one laws......Page 277 8.2 Basic notions......Page 284 8.3 Recurrence......Page 292 8.4 Fine structure......Page 302 8.5 Continuation......Page 312 9.1 Basic properties of conditional expectation......Page 324 9.2 Conditional independence ; Markov property......Page 336 9.3 Basic properties of smartingales......Page 348 9.4 Inequalities and convergence......Page 360 9.5 Applications......Page 374 1 Construction of measure......Page 389 2 Characterization of extensions......Page 394 3 Measures in R......Page 401 4 Integral......Page 409 5 Applications......Page 421 3. Probability theory......Page 427 5. Supplementary reading......Page 428 Index......Page 429 Since its publication by Academic Press, tens of thousands of students have taken a probability course using this classic textbook. Chung's A Course in Probability Theory, now in its third edition, has sustained its popularity for nearly 35 years. Originally developed from Dr. Chung's course at Stanford University, this book continues to be a successful tool for instructors and students alike. This third edition offers for the first time a supplement on Measure and Integral. This material has been used to supplement Dr. Chung's course for many years. It will assist students not previously exposed to this material and can also be sued as a review. The text is very flexible, offering instructors several different options in creating their syllabus, or in aligning it with current course design. It has been used successfully at over 75 universities since its initial publication. --back cover We begin with a discussion of distribution functions as a traditional way of introducing probability measures.