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Measure theory for analysis and probability

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Measure theory for analysis and probabilityby Alok Goswami, B.V. Rao.
作者:	Goswami, A.
其他作者:	Rao, B. V.
出版者:	Singapore :Springer Nature Singapore :2025.
面頁冊數:	x, 377 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Measure theory.
電子資源:	https://doi.org/10.1007/978-981-97-7929-1
ISBN:	9789819779291$q(electronic bk.)

Measure theory for analysis and probability
Goswami, A.

Measure theory for analysis and probability[electronic resource] /by Alok Goswami, B.V. Rao. - Singapore :Springer Nature Singapore :2025. - x, 377 p. :ill., digital ;24 cm. - Indian statistical institute series,2523-3122. - Indian statistical institute series..

1. Measure Theory: Why and What -- 2. Measures: Construction and Properties -- 3. Measurable Functions and Integration -- 4. Random Variables and Random Vectors -- 5. Product Spaces -- 6. Radon-Nikodym Theorem and Lp Spaces -- 7. Convergence and Laws of Large Numbers -- 8. Weak convergence and Central Limit Theorem -- 9. Conditioning: The Right Approach -- 10. Infinite Products -- 11. Brownian Motion: A Brief Journey.

This book covers major measure theory topics with a fairly extensive study of their applications to probability and analysis. It begins by demonstrating the essential nature of measure theory before delving into the construction of measures and the development of integration theory. Special attention is given to probability spaces and random variables/vectors. The text then explores product spaces, Radon-Nikodym and Jordan-Hahn theorems, providing a detailed account of spaces and their duals. After revisiting probability theory, it discusses standard limit theorems such as the laws of large numbers and the central limit theorem, with detailed treatment of weak convergence and the role of characteristic functions. The book further explores conditional probabilities and expectations, preceded by motivating discussions. It discusses the construction of probability measures on infinite product spaces, presenting Tulcea's theorem and Kolmogorov's consistency theorem. The text concludes with the construction of Brownian motion, examining its path properties and the significant strong Markov property. This comprehensive guide is invaluable not only for those pursuing probability theory seriously but also for those seeking a robust foundation in measure theory to advance in modern analysis. By effectively motivating readers, it underscores the critical role of measure theory in grasping fundamental probability concepts.

ISBN: 9789819779291$q(electronic bk.)

Standard No.: 10.1007/978-981-97-7929-1doiSubjects--Topical Terms:

182047
Measure theory.

LC Class. No.: QA312

Dewey Class. No.: 515.42

Measure theory for analysis and probability
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520 $a This book covers major measure theory topics with a fairly extensive study of their applications to probability and analysis. It begins by demonstrating the essential nature of measure theory before delving into the construction of measures and the development of integration theory. Special attention is given to probability spaces and random variables/vectors. The text then explores product spaces, Radon-Nikodym and Jordan-Hahn theorems, providing a detailed account of spaces and their duals. After revisiting probability theory, it discusses standard limit theorems such as the laws of large numbers and the central limit theorem, with detailed treatment of weak convergence and the role of characteristic functions. The book further explores conditional probabilities and expectations, preceded by motivating discussions. It discusses the construction of probability measures on infinite product spaces, presenting Tulcea's theorem and Kolmogorov's consistency theorem. The text concludes with the construction of Brownian motion, examining its path properties and the significant strong Markov property. This comprehensive guide is invaluable not only for those pursuing probability theory seriously but also for those seeking a robust foundation in measure theory to advance in modern analysis. By effectively motivating readers, it underscores the critical role of measure theory in grasping fundamental probability concepts.
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