About this document
Examples of Outer Measure in R² by Mayank Malhotra is a document available to read on EtoBox.
The document provides definitions and theorems related to the Caratheodory extension theorem. It begins by defining an outer measure and measurable sets according to Caratheodory. It then proves that the collection of Caratheodory measurable sets forms a sigma-algebra, and that the restriction of the outer measure to this sigma-algebra is a complete measure. It gives examples of applying this theorem to construct the Lebesgue measure on the real line.
- Author
- Mayank Malhotra
- Language
- EN