Preliminaries in Measure Theory

Related lectures (32)

Page 2 of 4

Explores harmonic forms on Riemann surfaces, covering uniqueness of solutions and the Riemann bilinear identity.

Covers the joint equidistribution of CM points and the ergodic decomposition theorem in compact abelian groups.

Covers the Cantor-Heine theorem, discussing uniform continuity and compactness.

Covers the concept of compact embedding in Banach spaces and Sobolev inequalities.

Covers continuous functions with compact support, density, and approximation, focusing on the heat equation.

Explores Banach spaces, emphasizing reflexivity and sequence convergence in a rigorous mathematical framework.

Explores the Stone-Weierstrass theorem, proving uniform density of specific function families on compact sets.

Explores the Darboux theorem for continuous functions on closed intervals, emphasizing uniform continuity and function behavior implications.

Explores Sobolev spaces in higher dimensions, discussing derivatives, properties, and challenges with continuity.

Explores the convergence of Fourier series in L² space with trigonometric polynomials and approximation theorems.