Concept

Borel set

Related lectures (32)

Covers the basics of sets and operations in mathematics, from set properties to advanced operations.

Delves into renormalization, fractals, and strange attractors, exploring the properties of countable and uncountable sets.

Explores countable and uncountable sets, Cantor set, Mandelbrot set, and Box dimension in nonlinear dynamics and complex systems.

Explores the construction of the Lebesgue function on the Cantor set and its unique properties.

Explores convolution, uniform continuity, Hilbert structure, and Lebesgue measure in analysis.

Explores independence in infinite coin tosses, covering sets, shifts, and T-invariance.

Covers the proof of unitary group uniqueness and spectral types.

Covers the extension of functional calculus to simple functions and the concept of *-homomorphism.

Explores the change of variables theorem in the plane, emphasizing boundedness and continuity of functions.

Explores inequalities for random variables, including Cauchy-Schwarz, Jensen, and Chebyshev.

Introduces measurable sets, functions, and the Cantor set properties, including ternary development of numbers.

Explores sub-sigma fields, random variables, and Borel measurable functions in probability theory.

Covers limits, continuity, open sets, and function extension by continuity with illustrative examples.

Covers the essentials of probability, algebras, and conditional probability, including the Borel o-algebra and Poisson processes.

Explores the continuity of mappings, paths between points, and centers of openings.

Covers advanced topics in analysis, including examples of sets, volume, Fubini's theorem, and integrability.

Covers Canonical Correlation Analysis, a method to find relationships between two sets of variables.

Explores the Lebesgue integral, where functions self-select partitions, leading to measurable sets and non-measurable complexities.

Explores open sets and interior points in real numbers, with examples and criteria for identification.

Covers manifolds, topology, smooth maps, and tangent vectors in detail.