1.1 Practicalities

Practical course arrangements.

1.2 Course overview

Introduction to course topics.

1.3 Sigma-algebras

Sigma-algebras are stable under complements and countable unions (and countable intersections).

1.4 Sigma-algebras vs topologies

Side note: How an abstract sigma-algebra differs from an abstract topology.

1.5 Examples of sigma-algebras

Examples and non-examples of sigma-algebras.

1.6 Generating sigma-algebras

An abstract method of defining a sigma-algebra containing the members of any particular set family.

1.7 Borel sigma-algebras

A Borel sigma-algebra is a sigma-algebra generated by open sets.



Alternative reading material

  • [Jacod & Protter, Chapters 1 and 2]
  • [Williams, Chapters 1.0, 1.1, 1.2 plus Chapter 0]


Last modified: Wednesday, 27 January 2021, 1:22 PM