New MT Article Ideas: Difference between revisions

From Optimal Transport Wiki
Jump to navigation Jump to search
No edit summary
 
(One intermediate revision by one other user not shown)
Line 9: Line 9:


==Measures==
==Measures==
* Lebesgue-Stieljes Measures
* Characterization of Finite Borel 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
* 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==
==Integration of Nonnegative Functions==

Latest revision as of 22:32, 19 December 2020

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

Analysis Fundamentals

  • Metric space vs. Pseudometric space

Measurable Sets

  • Product - 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

Integration of Nonnegative Functions

  • Key counterexamples


Modes of Convergence

  • Pointwise a.e. convergence
  • L1 convergence