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

• Product $\sigma$ - algebra
• Borel measureable sets vs. Lebesgue measurable sets

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