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[null,"1.","Record Nr.",null,"UNINA9910835058303321"]
[null,null,"Autore",null,"Shum Kenneth"]
[null,null,"Titolo",null,"Measure-Theoretic Probability : With Applications to Statistics, Finance, and Engineering / / by Kenneth Shum"]
[null,null,"Pubbl/distr/stampa",null,"Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2023"]
[null,null,"ISBN",null,"3-031-49830-5"]
[null,null,"Edizione",null,"[1st ed. 2023.]"]
[null,null,"Descrizione fisica",null,"1 online resource (262 pages)"]
[null,null,"Collana",null,"Compact Textbooks in Mathematics, , 2296-455X"]
[null,null,"Disciplina",null,"519.2"]
[null,null,"Soggetti",null,"Probabilities"]
[{"$nulls":4},"Measure theory"]
[{"$nulls":4},"Probability Theory"]
[{"$nulls":4},"Applied Probability"]
[{"$nulls":4},"Measure and Integration"]
[{"$nulls":4},"Teoria de la mesura"]
[{"$nulls":4},"Llibres electrònics"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,"Nota di contenuto",null,"Preface -- Beyond discrete and continuous random variables -- Probability spaces -- Lebesgue–Stieltjes measures -- Measurable functions and random variables -- Statistical independence -- Lebesgue integral and mathematical expectation -- Properties of Lebesgue integral and convergence theorems -- Product space and coupling -- Moment generating functions and characteristic functions -- Modes of convergence -- Laws of large numbers -- Techniques from Hilbert space theory -- Conditional expectation -- Levy’s continuity theorem and central limit theorem -- References -- Index."]
[null,null,null,"Sommario/riassunto","This textbook offers an approachable introduction to measure-theoretic probability, illustrating core concepts with examples from statistics and engineering. The author presents complex concepts in a succinct manner, making otherwise intimidating material approachable to undergraduates who are not necessarily studying mathematics as their major. Throughout, readers will learn how probability serves as the language in a variety of exciting fields. Specific applications covered include the coupon collector’s problem, Monte Carlo integration in finance, data compression in information theory, and more. Measure-Theoretic Probability is ideal for a one-semester course "]
[{"$nulls":4},"and will best suit undergraduates studying statistics, data science, financial engineering, and economics who want to understand and apply more advanced ideas from probability to their disciplines. As a concise and rigorous introduction to measure-theoretic probability, it is also suitable for self-study. Prerequisites include a basic knowledge of probability and elementary concepts from real analysis."]