Lectures related to Lebesgue measure

Analysis IV: Measurable Sets and Properties

Covers the concept of outer measure and properties of measurable sets.

Lebesgue Integration: Cantor Set

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

Analysis IV: Measurable Sets and Functions

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

Lebesgue Measure: Properties and Existence

Covers the properties of the Lebesgue measure and its existence.

Lebesgue Integral: Definition and Properties

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

The Riesz-Kakutani Theorem

Explores the construction of measures, emphasizing positive functionals and their connection to the Riesz-Kakutani Theorem.

Analysis IV: Convolution and Hilbert Structure

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

Lebesgue Integration: Simple Functions

Covers the Lebesgue integration of simple functions and the approximation of nonnegative functions from below using piecewise constant functions.

Independence and Products

Covers independence between random variables and product measures in probability theory.

Change of Variables Theorem in the Plane

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

Multivariable Integral Calculus

Covers multivariable integral calculus, including rectangular cuboids, subdivisions, Douboux sums, Fubini's Theorem, and integration over bounded sets.

Lebesgue Measure and Fourier Analysis

Explores Lebesgue measure, Fourier analysis, PDE applications, and optimal transport in PDEs.

Determinantal Point Processes and Extrapolation

Covers determinantal point processes, sine-process, and their extrapolation in different spaces.

Circular Trigonometry: Understanding Geometric Angles

Explores the concept of angles in circular trigonometry, emphasizing geometric angles and their properties.

Introduction to Quantum Chaos

Covers the introduction to Quantum Chaos, classical chaos, sensitivity to initial conditions, ergodicity, and Lyapunov exponents.

Probability Theory: Lecture 2

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

Simon's Problem

Discusses Simon's Problem and deterministic computation through various equations and implications.

Lebesgue Integral: Properties and Convergence

Covers the Lebesgue integral, properties, and convergence of functions.

Analysis: Measure and Integration

Introduces the course on measure and integration, focusing on developing a new theory to overcome the limitations of the Riemann integral.

Effective Field Theory: Testing Weak Interactions

Explores effective field theory for testing weak interactions and parity violation through forward-backward asymmetry.