Measure Theory Courses and Certifications

International Centre for Theoretical Sciences

Particle Methods for Optimization Over Measures - Lecture 2

Explore particle methods for measure optimization in this advanced lecture, covering theoretical foundations and practical applications in data science and machine learning.

• YouTube
• 53 minutes
• On-Demand
• Free Video

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 Video

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 Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

A Lorentzian Analog for Hausdorff Dimension and Measure

Explore a novel approach to geometric dimension in Lorentzian spaces, comparing it to Hausdorff dimension and examining applications in spacetime analysis and synthetic curvature bounds.

• YouTube
• 36 minutes
• On-Demand
• Free Video

Centre de recherches mathématiques - CRM

Divisibility of Spheres with Measurable Pieces - Oleg Pikhurko

Explore divisibility of spheres with measurable pieces, focusing on Euclidean (d-1)-dimensional sphere S^(d-1) and special orthogonal matrices. Examine impossibility of measurable divisibility for generic rotations.

• YouTube
• 48 minutes
• On-Demand
• Free Video

Banach Center

Invariant and Quasi-Invariant Measures for Actions of Oligomorphic Groups - Part II

Explore advanced concepts of invariant and quasi-invariant measures in oligomorphic group actions, building on Part I's foundations.

• YouTube
• 1 hour
• On-Demand
• Free Video

Banach Center

Invariant and Quasi-Invariant Measures for Actions of Oligomorphic Groups - Part 3

Explore advanced concepts in measure theory, focusing on invariant and quasi-invariant measures for oligomorphic group actions in this advanced mathematics lecture.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

Banach Center

Invariant and Quasi-Invariant Measures for Actions of Oligomorphic Groups - Part I

Explore invariant and quasi-invariant measures for oligomorphic group actions, delving into advanced mathematical concepts and theories.

• YouTube
• 58 minutes
• On-Demand
• Free Video

Simons Semester on Dynamics

One-Parameter Families of Hyperbolic Iterated Function Systems on the Line - Lecture 3

Delve into hyperbolic iterated function systems and their dimensional properties, exploring transversality methods for analyzing one-parameter families and their applications in measure theory and dynamics.

• YouTube
• 1 hour 31 minutes
• On-Demand
• Free Video

Kyoto-U OCW - Unofficial

面積0の集合と関連する問題 - 2021年4月

Dive into 面積0の集合の数学的探究、Hausdorff測度と次元の概念、そして掛谷予想について学ぶ数学フロンティア講座。

• YouTube
• 25 minutes
• On-Demand
• Free Video

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 Video

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 Video

International Centre for Theoretical Sciences

Particle Methods for Optimization Over Measures - Lecture 2

Explore particle methods for measure optimization, focusing on theoretical foundations and practical applications in data science and machine learning.

• YouTube
• 2 hours 19 minutes
• On-Demand
• Free Video