Carathéodory's measure extension theorem
Teorema de extensión de medidas de Carathéodory
- Date
- 1914-1918 · confidence high
- Place
- Göttingen, Lower Saxony, Germany
- Credited to
- Constantin Carathéodory
- Field
- Knowledge & symbols
What was discovered
He introduced the outer measure and the measurability criterion that allow a measure defined on an algebra to be extended to a σ-algebra. It is the basis of Lebesgue measure and of measure in probability.
The criterion appeared in 1914 (Göttinger Nachrichten) and the theorem was spread by Vorlesungen über reelle Funktionen (1918). Carathéodory was born in Berlin to a Greek family from Constantinople.
What it led to
- Kolmogorov's axiomatic probability
- abstract integration