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Spring 2000
MAT 571
REAL ANALYSIS II

Instructor:  Jack Spielberg
Time:  MWF, 11:40 - 12:30
Location:  PSF-207
Line Number:  85612

Course Description:

This is the second half of a basic graduate level 
course in real analysis.  The topics to be covered are:

(*) Fourier transform on L^1(R) and L^2(R), and Fourier inversion.
(*) Introduction to general topology, including the Arzela-Ascoli
     theorem, the Stone-Weierstrass theorem, and the Baire category
     theorem.
(*) Introduction to functional analysis.
(*) Radon measures and the dual space of C_0(X).
(*) Introduction to ergodic theory.  I hope to cover ergodicity,
      entropy of measurable transformations, and topological
      entropy if time permits.

There will be occasional homework assignments and no exams.

Prerequisites:

Familiarity with the Lebesgue integral on the reals will suffice for much 
of the course.  For the section dealing with Radon measures, an 
acquaintance with abstract measure theory (e.g. as presented in chapters
1 and 2 of Folland) will be helpful.

Textbook (optional):  Any graduate level book on real analysis is 
suitable.  Examples are:  Folland, McDonald-Weiss, Jones, Royden.  The 
lectures will be self-contained, so that no textbook is required.