Description
Book Synopsis: This contemporary first course focuses on concepts and ideas of Measure Theory, highlighting the theoretical side of the subject. Its primary intention is to introduce Measure Theory to a new generation of students, whether in mathematics or in one of the sciences, by offering them on the one hand a text with complete, rigorous and detailed proofs--sketchy proofs have been a perpetual complaint, as demonstrated in the many Amazon reader reviews critical of authors who "omit 'trivial' steps" and "make not-so-obvious 'it is obvious' remarks." On the other hand, Kubrusly offers a unique collection of fully hinted problems. On the other hand, Kubrusly offers a unique collection of fully hinted problems. The author invites the readers to take an active part in the theory construction, thereby offering them a real chance to acquire a firmer grasp on the theory they helped to build. These problems, at the end of each chapter, comprise complements and extensions of the theory, further examples and counterexamples, or auxiliary results. They are an integral part of the main text, which sets them apart from the traditional classroom or homework exercises.
JARGON BUSTER: measure theory
Measure theory investigates the conditions under which integration can take place. It considers various ways in which the "size" of a set can be estimated.
This topic is studied in pure mathematics programs but the theory is also foundational for students of statistics and probability, engineering, and financial engineering.
Designed with a minimum of prerequisites (intro analysis, and for Ch 5, linear algebra)
Includes 140 classical measure-theory problems
Carefully crafted to present essential elements of the theory in compact form
Details
Are you a student or professional looking to dive into the world of Measure Theory? Look no further than our comprehensive book, "Measure Theory: A First Course". This contemporary first course is designed to introduce Measure Theory to a new generation of students. With complete, rigorous, and detailed proofs, we address the perpetual complaint of sketchy proofs found in many other textbooks. We understand the importance of not omitting 'trivial' steps and avoiding not-so-obvious 'it is obvious' remarks.
What sets our book apart is the unique collection of fully hinted problems. We believe that active engagement with the theory leads to a firmer grasp and deeper understanding. That's why we invite our readers to take an active part in the theory construction, offering them a real chance to acquire knowledge as they help build the theory. At the end of each chapter, you'll find a comprehensive set of complements, extensions, examples, counterexamples, and auxiliary results. These problems are an integral part of the main text, setting us apart from traditional classroom or homework exercises.
But what exactly is Measure Theory? It investigates the conditions under which integration can take place and considers various ways to estimate the "size" of a set. This foundation theory is not only crucial for students of mathematics but also for those studying statistics and probability, engineering, and financial engineering.
With a minimum of prerequisites (intro analysis, and for Ch 5, linear algebra), our book is accessible to a wide range of students and professionals. Additionally, with 140 classical measure-theory problems, you'll have ample opportunities to practice and reinforce the essential elements of the theory. Don't miss out on this compact and comprehensive guide to Measure Theory. Order your copy of "Measure Theory: A First Course" today!
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