Lecturer

Prof. Boris Tsirelson (School of Mathematical Sciences).

Prerequisites

Be acquainted with such things as the Hilbert space L₂ of square integrable functions on a measure space. Everything else will be explained from scratch. However, some maturity in analysis is needed. (Maturity in probability is not needed.)

Grading policy

Written homework and oral exam.

Lecture notes

1. Foreword.
1. Basic notions and constructions.
2. Probability, random elements, random sets.
3. Topology as a powerful helper.
4. From random Borel functions to random closed sets.
5. Random connected components.
6. Borel sets in the light of analytic sets.
7. Equivalence relations and measurability.

Additional sources

Relevant articles in Encyclopedia of Mathematics wiki:

• Measurable space,
• Standard Borel space,
• Measure space,
• Measure algebra,
• Universally measurable,
• Analytic Borel space.