Lectures related to Newtonian Potential: Bounded Domains

Covers examples of direct and indirect proofs in mathematics.

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

Explores geodesic convexity in metric spaces and its applications, discussing properties and the stability of inequalities.

Covers the Fourier inversion formula, exploring its mathematical concepts and applications, emphasizing the importance of understanding the sign.

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

Covers the Central Limit Theorem and its application to random variables, proving convergence to a normal distribution.

Covers proof techniques including direct proof, contraposition, contradiction, cases, and counterexample.

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.