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Lecture
Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.
This lecture covers the construction of measures, focusing on positive functionals and their inner and outer measures. It discusses the properties of o-additivity, measurability of sets, and the concept of a measurable collection. The lecture also presents propositions related to measurable disjoint sets and concludes with the Riesz-Kakutani Theorem, which establishes the existence of a regular and complete measure on a Borel o-algebra. The theorem connects positive functionals to measures, showcasing the significance of the Lebesgue measure in this context.