### materials

I have the generous permission by Greg Hjorth to
use his notes on Measure Theory.

You can also watch all of Marty Ross's AMSI lectures in 2006 by following the link
on this page.

We participate in the CARMA-AMSI short course on Haar measure given by Joe Diestel. Lecture notes and other materials can be found here.

### links

Measure Theory on Eric Weisstein's World of Mathematics

Haar Measure on Eric Weisstein's World of Mathematics

Ergodic Theory on Eric Weisstein's World of Mathematics

### course description

I intend to follow Greg's notes, augmenting and subtracting
material from time to time.

Ideally, I'd like to cover the
following notions, topics and examples:

Notions:
Inner and outer measures; Vitali covering theorem, Lebesgue measure,
Hausdorff dimension.
Change of variables.
Proofs by approximation.
Convergence theorems.
Radon-Nikodym theorem and conditional approximation.
Product measures and Fubini-Tonelli theorem.

Selected topics from ergodic theory (such as invariant measures, Haar measure, Poincaré
recurrence theorem) and from geometric measure theory (such as the area and
co-area formulas).

Examples:
Hamiltonian dynamics, Bernoulli shifts, rotations of the circle,
horocycle flow on a hyperbolic surface, Hausdorff dimension of a fractal
set.

This is, of course, more material than can be covered in 13 weeks, but
it gives us a menu to choose from.

### learning activities

Mo 09:00-09:50 67-641 (lecture)
Tu 11:00-11:50 67-641 (lecture/tutorial)
Th 14:00-15:50 67-442 (lecture/tutorial))
### consultation hours

WE 11:00-11:50 67-710
FR 10:00-10:50 67-710
### problem sets (pdf)

Problem Set 1
Problem Set 2
Problem Set 3
Problem Set 4
Problem Set 5
Problem Set 6
### assignments (pdf)

Assignment 1 (due Thursday, 12 August)
Assignment 2 (due Monday, 6 September)
Assignment 3 (due Monday, 4 October)
Assignment 4 (due Monday, 25 October)
### final exam

TBA
(10 min perusal; 120 min duration)
### general references

"Real Analysis" by Halsey L. Royden (Wiley, 1989)
"Real and Complex Analysis" by Walter Rudin (McGraw-Hill, 1986)
"Counterexamples in analysis" by Bernard R. Gelbaum and John M.H. Olmsted (Holden-Day, 1964)
### specialised references

"Measure Theory and Fine Properties of Functions" by Lawrence
C. Evans and Ronald F. Gariepy (CRC Press, 1992)
"Geometric measure theory: a beginner's guide" by Frank Morgan (Academic Press, 1988)
"Ergodic theory" by Karl Petersen (Cambridge University Press, 1983)
"The geometry of fractal sets" by K.J. Falconer (Cambridge University Press, 1984)