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Elements of Measure and Probability

This book can serve as a first course on measure theory and measure theoretic probability for upper undergraduate and graduate students of mathematics, statistics and probability. Starting from the basics, the measure theory part covers Caratheodory’s theorem, Lebesgue–Stieltjes measures, integratio...

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Bibliografiske detaljer
Hovedforfatter: Bose, Arup (Author)
Institution som forfatter: SpringerLink (Online service)
Format: Electronisk eBog
Sprog:engelsk
Udgivet: Singapore : Springer Nature Singapore : Imprint: Springer, 2025.
Udgivelse:1st ed. 2025.
Serier:Texts and Readings in Mathematics, 88
Fag:
Measure theory.
Probabilities.
Measure and Integration.
Probability Theory.
Online adgang:https://doi.org/10.1007/978-981-95-2758-8
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Indholdsfortegnelse:
  • Preliminaries
  • Classes of Sets
  • Introduction to Measures
  • Extension of Measures
  • Lebesgue-Stieltjes Measures
  • Measurable Functions
  • Integral
  • Basic Inequalities
  • Lp Spaces: Topological Properties
  • Product Spaces and Transition Measures
  • Random Variables and Vectors
  • Moments and Cumulants
  • Further Modes of Convergence of Functions
  • Independence and Basic Conditional Probability
  • 0-1 Laws
  • Sums of Independent Random Variables
  • Convergence of Finite Measures
  • Characteristic Functions
  • Central Limit Theorem
  • Signed Measure
  • Randon-Nikodym Theorem
  • Fundamental Theorem of Calculus
  • Conditional Expectation.

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