Mathematics 750-751: Analysis I,II

Mathematics 750-751: Analysis I,II

General Information:

Title:	Mathematics 750-751: Analysis I,II
Credits:	3 credits each
Prerequesites:	Mathematics 451
Required for:	Mathematics 754-755 Mathematics 760-761 Mathematics 762-763 Mathematics 784-785
Suggested Text:	Royden. Real Analysis. Macmillan Publishing Co., Inc.

Course Description:

Lebesgue and general measure and integration theory, differentiation, product spaces, metric spaces, elements of classical Banach spaces, Hilbert spaces, and selected advanced topics.

Outline:

Chapter I.	Preliminaries	Set theory, sturcture of R.
Chapter II.	Measures	Algebra of sets, measures and outer measures, construction of outer measures and measures, copmletion of measures, the Lebesgue measure, signed measures.
Chapter III.	Integration	Measureable funcitons, convergence a. e., almost uniform, and in measure, Egeroff's theorem, integrable functions, sequences of integrable funcitons and convergence theorems and Fatou's Lemma, Riemann vss Lebesgue's integral.
Chapter IV.	Differentiability	Absolute continuity of measures, Radon'Nidokym theorem, Lebesgue decomposition, differentiation theorem.
Chapter V.	Product Spaces	Product of measures, Fubini's theorem.

Goals:

Current Syllabus (Fall 1999-2000)

Ayse Sahin (Fall 1999)

Note:

Special Needs: "Any students with disabilities or other special needs, who need special accommodations in the course, are invited to share these concerns or requests with the instructoras soon as possible."
Academic Honesty: All work in this course must be completed in a manner consistent with NDSU University Senate Policy, Section 335: Code of Academic Responsibility and Conduct.

Last Modified: October 23, 1999
ndsu_math@ndsu.nodak.edu