Section outline

    • Class 1, sept 30, 2025 File

      Sigma algebras: definition and examples. Abstract measures: definition and examples.

    • Class 2, oct. 1, 2025 File

      Counting measure. Properties of abstract measures: monotonicity, finite additivity and measure of the union/difference, continuity from below and from above, examples.

      lebesgue measure: introduction, intervals, definition of outer measure.

    • Class 3, oct 3, 2025 File

      Exercises on abstract measures. Countable sub-additivity. Lebesgue outer measure, main properties.

    • Class 4, oct 6, 2025 File

      Lebesgue class, basic facts and properties. Measurable functions: definition and examples (indicator and simple functions). 

    • Class 5, oct 7, 2025 File

      Properties of measurable functions.

    • Class 6, oct 10, 2025 File

      Exercises on Lebesgue measure. 
      definition of integral.

    • Class 7, oct 13, 2025 File

      Definition of integral. Chebichev inequality.