Measure Theory Wiki

Welcome to the Measure Theory Wiki!

Here are some New MT Article Ideas

Real Analysis Background

• Key Topics from Undergraduate Analysis
• Lower semicontinuous functions

Measure Theory

• Algebra
• Approximation by Open/Compact Sets
• $\sigma$-algebra
• Inner measure
• Outer measure
• Measures
• Absolutely Continuous Measures
• Borel-Cantelli Lemma
• Banach-Tarski Paradox <-- this would be a great article for someone to edit; while it is very well written, it lacks references.
• Measurable function
• Intersections of Open Sets and Unions of Closed Sets (${\mathcal {G}}^{\delta }$ and ${\mathcal {F}}^{\sigma }$ sets)
• Cantor Set
• Cantor Function
• Simple Function
• Monotone Convergence Theorem
• Beppo-Levi Theorem
• Fatou's Lemma
• Egerov's Theorem/Bounded Convergence Theorem
• Dominated Convergence Theorem
• Isomorphism of Measure Spaces
• L1 Space
• Lusin's Theorem
• Caratheodory's Theorem
• Convergence in Measure
• Modes of Convergence
• Borel $\sigma$-algebra and ${\mathcal {B}}_{\mathbb {R} }$
• [[Vitali's Theorem and non-existence of a measure on $2^{\mathbb {R} }$]]

Other

• 201A Distraction Recommendations
• Optimal Transport Wiki
• Nonlocal Equations Wiki
• Proteopedia
• Quantum Information Wiki