(BQ) The book is largely about the Lebesgue theory of integration, but includes a very thorough coverage of the theory of metric and topological spaces in the first two chapters. Chapters 3,4 and 5 are the heart of the book covering measure theory, the Lebesgue integral and some topics from introductory functional analysis like theory of operators and Banach spaces.
Part 1 ebook Measure and integration problems with solutions included: Measure on a σ-Algebra of Sets, Lebesgue Measure on R, Measurable Functions, Convergence a.e. and Convergence in Measure, Integration of Bounded Functions on Sets of Finite Measure, Integration of Nonnegative Functions.
Part 2 ebook Measure and integration problems with solutions included: Integration of Measurable Functions, Signed Measures and Radon-Nikodym Theorem, Differentiation and Integration, L p Spaces, Integration on Product Measure Space, Some More Real Analysis Problems.
Lectures on Measure Theory and Probabilityby H.R. PittPublisher: Tata institute of Fundamental Research 1958Number of pages: 126Description:Measure Theory (Sets and operations on sets, Classical Lebesgue and Stieltjes measures, The Lebesgue integral ...); Probability (Function of a random variable, Conditional probabilities, The Central Limit Problem, Random Sequences and Convergence Properties
This is the second volume containing examples from Functional analysis. The topics here are
limited to Topological and metric spaces, Banach spaces and Bounded operators.
Unfortunately errors cannot be avoided in a first edition of a work of this type. However, the author
has tried to put them on a minimum, hoping that the reader will meet with sympathy the errors
which do occur in the text.
(BQ) With the success of its previous editions, Principles of Real Analysis, Third Edition, continues to introduce students to the fundamentals of the theory of measure and functional analysis. In this thorough update, the authors have included a new chapter on Hilbert spaces as well as integrating over 150 new exercises throughout. The new edition covers the basic theory of integration in a clear, well-organized manner, using an imaginative and highly practical synthesis of the "Daniell Method" and the measure theoretic approach.
(BQ) Problems in Real Analysis is the ideal companion for senior science and engineering undergraduates and first-year graduate courses in real analysis. It is intended for use as an independent source, and is an invaluable tool for students who wish to develop a deep understanding and proficiency in the use of integration methods.
The lecture notes are organized as follows: Chapter 1 gives a concise
overview of the theory of Lebesgue and Stieltjes integration and convergence
theorems used repeatedly in this course. For mathematic students,
familiar e.g. with the content of Bauer (1996) or Bauer (2001),
this chapter can be skipped or used as additional reference .
Chapter 2 follows closely F¨ollmer’s approach to Itˆo’s calculus, and is
to a large extent based on lectures given by him in Bonn (see Foellmer
(1991)). A motivation for this approach is given in Sect. 2.1.