New MT Article Ideas: Difference between revisions

Latest revision as of 22:32, 19 December 2020

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

Characterization of Finite Borel Measures
Result connecting the absolute continuity of a Borel measure with respect to the Lebesgue measure with absolutely continuous functions

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 ==Analysis Fundamentals==
+* Metric space vs. Pseudometric space
 ==Measurable Sets==
-* Vitali's Theorem and non-existence of a measure on <math>2^\mathbb{R}</math>
-* Borel <math>\sigma</math>-algebra and <math>\mathcal{B}_\mathbb{R}</math>
-* <math>\mathcal{F}^\sigma</math> and <math>\mathcal{G}^\delta</math> sets
 * Product <math> \sigma </math> - algebra
 * Borel measureable sets vs. Lebesgue measurable sets
 ==Measures==
-* Caratheodory's Theorem
-* Isomorphism of Measure Spaces
-* Lebesgue-Stieljes Measures
 * Characterization of Finite Borel Measures
-* Approximation by Open/Compact Sets
+* Result connecting the absolute continuity of a Borel measure with respect to the Lebesgue measure with absolutely continuous functions
-* Cantor set
-* Cantor function
-==Measurable Functions==
+==Integration of Nonnegative Functions==
-* Simple functions
+* Key counterexamples
+==Modes of Convergence==
+* Pointwise a.e. convergence
+* L1 convergence