2007 Fall MATH 241-01
Bulletin Course Description Measures; Lebesgue integral; L<^>p spaces; Daniell integral, differentiation theory, product measures. Instructor: Staff
(Instructor named in bulletin description above may not be current. For current instructor, see listing below.)
Title REAL ANALYSIS Department MATH Course Number 2007 Fall 241 Section Number 01 Primary Instructor Beale,James T Permission required? N
Prerequisites
Mathematics 204 or equivalent.
Synopsis of course content
This course develops measure theory and Lebesgue integration. This theory is foundational for much of analysis and in particular for the mathematical theory of probability. This course is a natural beginning part of a graduate program in mathematics. Besides measure theory and integration (as in Chapters 1--6, 11, and 12 in Royden's book, mentioned below), we include a brief treatment of Fourier series and transforms, and the formulation of probability theory in terms of measure theory, including proofs of basic theorems such as the Central Limit Theorem. The main prerequisite is a rigorous undergraduate course in real analysis. Students should have a working knowledge of the concepts from undergraduate analysis and should be used to writing proofs in analysis.
Textbooks
The textbook is not yet decided, but in the past we have
used Real Analysis by H. Royden, third edition, with supplementary notes
on probability and on Fourier series and transforms.
Assignments
There will be weekly written assignments.
Exams
There will be a final exam. There may be a midterm exam.
Term Papers
None.
Grade to be based on
Homework and exam(s).
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