Lectures related to Sigma-additive set function

Introduces Cartesian product and induction for proofs using integers and sets.

Covers the proof of theorem 4.2 on multiplicities and the special structure of local rings at a simple point of a plane.

Explores interior points, closures, and set properties in real analysis.

Explores ergodic theory, spectral operators, and almost periodic factors in dynamical systems and spectral theory.

Explores conditional expectation, the grouping lemma, and the law of large numbers.

Covers properties of sets of measure zero, integrability criteria, and Fubini's theorem.