Measure and category
2013/2014, sem. 1
- Prof. Boris Tsirelson
(School of Mathematical Sciences).
- Time and place
- Monday 16-17 Ornstein 102
- Wednesday 16-18 Ornstein 110
- Be acquainted with Lebesgue integration and metric spaces.
Everything else will be explained from scratch. However, some
maturity in analysis is needed.
- Grading policy
- Written homework and oral exam.
About Egorov's and Lusin's theorems.
Fubini's theorem and Kuratowski-Ulam theorem.
More on differentiation.
Typical compact sets.
Typical functions via Banach spaces.
Typical functions like to embed.
- Basic ideas.
- Typical sequences etc.
- The Banach-Mazur game.
- Choice axioms and Baire category theorem.
- Many points of continuity.
- Good sets and their equivalence classes.
A. M. Bruckner, J. B. Bruckner, and B. S. Thomson,
Analysis (2nd Edition),
(2008). (See Chapter 10.)
John Oxtoby, "Measure and category (a survey of the analogies
between topological and measure spaces)", Springer 1971.
The Baire category is a profound triviality which condenses the folk wisdom of a generation of ingenious mathematicians into a single statement.
T.W. Körner, "Linear analysis" Sect.6, p.13.