Arzelà–Ascoli theorem
Teorema de Arzelá-Ascoli
- Date
- 1883-1895 · confidence medium
- Place
- Bologna, Emilia-Romagna, Italy
- Credited to
- Giulio Ascoli y Cesare Arzelà
- Field
- Knowledge & symbols
What was discovered
Functional analysis theorem giving the necessary and sufficient conditions (equicontinuity and boundedness) for a family of continuous functions to have a uniformly convergent subsequence; a foundational tool in analysis and differential equations.
What it led to
- theory of compact function spaces
- existence of solutions to differential equations (Peano)
- modern functional analysis
- theory of compact operators