New MT Article Ideas: Difference between revisions
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==Measurable Sets== | ==Measurable Sets== | ||
* Vitali's Theorem and non-existence of a measure on <math>2^\mathbb{R}</math> | * Vitali's Theorem and non-existence of a measure on <math>2^\mathbb{R}</math> | ||
* Product <math> \sigma </math> - algebra | * Product <math> \sigma </math> - algebra | ||
* Borel measureable sets vs. Lebesgue measurable sets | * Borel measureable sets vs. Lebesgue measurable sets | ||
Revision as of 20:22, 18 December 2020
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
- Product - 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