Lectures related to Second-countable space

Covers selected topics in mathematics, including Taylor approximations and algebraic structures of Z and K[X].

Explores countability and undecidable problems in the theory of computation.

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Explores negligible sets, integrable sets, and almost everywhere concept in mathematical analysis.

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

Explores toy models, sigma-algebras, T-valued random variables, measures, and independence in probability theory.

Covers the properties of the Lebesgue measure and its existence.