Lecture 1 | Motivation: the strong law of large numbers. Preliminary notions from set theory: countable and uncountable sets, algebra of sets. | Slides |

Lecture 2 | Construction of measures: Caratheodory’s theorem. Application to the infinite coin toss example. Non-measurable sets. | Slides, Video |

Lecture 3 | Applications: the strong law of large numbers for infinite coin tosses. | Slides, Video |

Lecture 4 | Integral: Measurable functions. The Lebesgue integral. The basic convergence theorems. | Slides, Video |

Lecture 5 | Conditional expectations: Using σ-algebras to model information. Definition of conditional expectations and its basic properties. | Slides, Video |

Lecture 6 | Large economies: Using measure theory to model competitive equilibrium in economies with a continuum of agents. Definitions and basic results. | Slides, Video |

# July 2020 measure theory lectures

Jul. 24, 2020

I completed by online measure theory lectures today. Thanks to all those who participated. Here’s an archive of the content.