Measure Theory Courses and Certifications

Hausdorff Center for Mathematics

Is There a Triangle Inequality for Measures of Compact, Convex Sets?

Explore geometric inequalities for convex bodies, focusing on surface area, Minkowski sums, and measure properties. Examine recent findings on monotonicity and supermodularity for Borel and Radon measures.

• YouTube
• 25 minutes
• On-Demand
• Free Online Course

Hausdorff Center for Mathematics

Building Measure Theory Using Hierarchy Builder

Explore the Hierarchy Builder DSL for Coq and its application in constructing measure theory and Lebesgue measure, with insights for potential adaptations to other proof assistants.

• YouTube
• 40 minutes
• On-Demand
• Free Online Course

Measure Theory

Comprehensive exploration of measure theory, covering abstract measures, Lebesgue integration, Borel measures, Lp spaces, and classical theorems. Ideal for advanced mathematics students seeking in-depth understanding.

• Swayam
• 12 weeks
• On-Demand
• Free Online Course

IMSC;  NPTEL

Measure and Integration

Explore abstract measures, Lebesgue integration, and L^p spaces in this advanced mathematics course. Covers key theorems, convergence, product spaces, and applications in analysis.

• Swayam
• 12 weeks
• On-Demand
• Free Online Course

The Bright Side of Mathematics

Measure Theory

Comprehensive exploration of measure theory, covering sigma algebras, Lebesgue measures, integrals, convergence theorems, and advanced concepts like product measures and Fubini's theorem.

• YouTube
• 5 hours
• On-Demand
• Free Online Course

Friedrich–Alexander University Erlangen–Nürnberg

Quantum Theory

Comprehensive exploration of quantum mechanics, covering axioms, mathematical foundations, operators, spectra, and applications like spin and harmonic oscillators. Ideal for advanced physics students.

• YouTube
• 1 day 15 hours
• On-Demand
• Free Online Course

Hausdorff Center for Mathematics

On Some Tight Convexity Inequalities for Symmetric Convex Sets

Explores tight convexity inequalities for symmetric convex sets, focusing on Gaussian measure, isoperimetric problems, and Dirichlet-Poincare inequality. Discusses progress using L2 methods and energy minimization.

• YouTube
• 40 minutes
• On-Demand
• Free Online Course

ICTP Mathematics

Introduction to Ergodic Theory 1

Explore measure theory fundamentals, sigma algebras, and Lebesgue measure construction in this comprehensive introduction to ergodic theory.

• YouTube
• 48 minutes
• On-Demand
• Free Online Course

Hausdorff Center for Mathematics

On Density of Sobolev Functions on Euclidean Domains

Explore recent findings on Sobolev space density, removability of measure zero sets, and extension operators in Euclidean domains. Gain insights into advanced mathematical concepts and their applications.

• YouTube
• 45 minutes
• On-Demand
• Free Online Course

Hausdorff Center for Mathematics

Guido De Philippis - PDE Constrained Measures III

Explore advanced concepts in PDE-constrained measures with Guido De Philippis, delving into complex mathematical theories and applications in this advanced lecture.

• YouTube
• 35 minutes
• On-Demand
• Free Online Course

Applied Algebraic Topology Network

Vietoris-Rips Thickenings - Problems for Birds and Frogs

Explore open problems in Vietoris-Rips complexes, connecting diverse mathematical areas. Suitable for both broad theorists and problem-solving specialists in applied algebraic topology.

• YouTube
• 1 hour 18 minutes
• On-Demand
• Free Online Course

Joint Mathematics Meetings

Measuring Singularities - Colloquium 2

Explore advanced mathematical concepts in singularity theory with Karen E. Smith, delving into measurement techniques and their applications in algebraic geometry.

• YouTube
• 46 minutes
• On-Demand
• Free Online Course

Insights into Mathematics

The Curious World of Integral Polynumbers - Math Foundations 233

Explore integral polynumbers through particle physics concepts, expanding arithmetic to include integers as coefficients and exponents, and viewing polynomials as algebraic objects rather than functions.

• YouTube
• 37 minutes
• On-Demand
• Free Online Course

Insights into Mathematics

Computability and Problems with Set Theory - Math History

Explores historical controversies in set theory, Gödel's incompleteness theorems, Zermelo-Fraenkel axioms, and Turing's computability concepts, challenging traditional views on infinite sets in mathematics.

• YouTube
• 47 minutes
• On-Demand
• Free Online Course

Alan Turing Institute

Semantic Models for Higher-Order Bayesian Inference - Sam Staton, University of Oxford

Explore probabilistic programming for Bayesian modeling, focusing on advanced languages with higher-order functions and continuous distributions. Learn about quasi-Borel spaces and modular inference algorithms.

• YouTube
• 41 minutes
• On-Demand
• Free Online Course