What did Carathéodory develop in measure theory?
Carathéodory's Extension Theorem
Measure Distribution Theory
Measure Optimization
Measure Dynamics
Answer
Carathéodory's Extension Theorem, developed by Constantin Carathéodory, provides a fundamental result in measure theory. It establishes that any finitely additive measure defined on a field of subsets of a set can be extended to a countably additive measure on the sigma-algebra generated by the field. This theorem is crucial in constructing measures on complex sets and is widely used in probability theory, statistics, and other fields.
Mastering the Mind of Constantin Carathéodory: A Mathematical Adventure
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