## Real Analysis and ProbabilityThis classic text offers a clear exposition of modern probability theory. |

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#### LibraryThing Review

User Review - Tobias.Bruell - LibraryThingDISCLAIMER: I only read most of the non-starred sections and did only few of the exercises. The first half of the book covers real analysis (i.e., topological and metric spaces, measure and ... Read full review

### Contents

Foundations Set Theory | 1 |

General Topology | 24 |

Measures | 85 |

Integration | 114 |

LР Spaces Introduction to Functional Analysis | 152 |

Convex Sets and Duality of Normed Spaces | 188 |

Measure Topology and Differentiation | 222 |

Introduction to Probability Theory | 250 |

Convergence of Laws and Central Limit Theorems | 282 |

Conditional Expectations and Martingales | 336 |

Convergence of Laws on Separable Metric Spaces | 385 |

Stochastic Processes | 439 |

Measurability Borel Isomorphism and Analytic Sets | 487 |

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### Common terms and phrases

algebra assume axiom Borel a-algebra Borel measurable Borel set bounded Brownian motion called cardinality Cartesian product Cauchy characteristic function closed set compact sets complete continuous function Corollary countably additive cr-algebra defined definition dense disjoint distribution function equivalent ergodic example extended finite measure finite set follows function F given gives Hausdorff space Hilbert space Hint implies independent inequality infinite inner product integral intersection Kolmogorov large numbers Lebesgue measure Lemma Let F linear Markov martingale Math measurable function measurable sets measure space metric space non-empty nonnegative norm open sets orthonormal probability measure probability space Problem product topology proof of Theorem Proposition proved random variables real functions real numbers real-valued function separable metric space sequence Show submartingale subsets Suppose Theorem Let topological space uncountable uniformly union unique values vector space