New MT Article Ideas

Here is a list of new article ideas for the Measure Theory Wiki.

Analysis Fundamentals

• Metric space vs. Pseudometric space

Measurable Sets

• Vitali's Theorem and non-existence of a measure on $2^{\mathbb {R} }$
• Borel $\sigma$-algebra and ${\mathcal {B}}_{\mathbb {R} }$
• Product $\sigma$ - algebra
• Borel measureable sets vs. Lebesgue measurable sets

Measures

• Lebesgue-Stieljes Measures
• Characterization of Finite Borel Measures
• Result connecting the absolute continuity of a Borel measure with respect to the Lebesgue measure with absolutely continuous functions
• Approximation by Open/Compact Sets

Integration of Nonnegative Functions

• Key counterexamples

Modes of Convergence

• Pointwise a.e. convergence
• L1 convergence
• Egorov's theorem