Measure theory and Lebesgue integral
Teoría de la medida e integral de Lebesgue
- Date
- 1902 · confidence high
- Place
- Paris and Nancy, France
- Credited to
- Henri Lebesgue (thesis, 1902); earlier work by Borel and Jordan
- People
- 👤 Camille Jordan1838–1922👤 Henri Léon Lebesgue1875–1941
- Field
- Knowledge & symbols
What was discovered
The definition of the measure of sets and of an integral that behaves well with limits, extending Riemann's. It is the framework of modern analysis and axiomatic probability.
Lebesgue explained the idea with the image of counting coins by grouping them by value rather than in order.
What it led to
- Kolmogorov's axiomatics
- functional analysis and L^p spaces
- harmonic analysis
- ergodic theory
Built on
- Fourier series and transform1807
- Set theory and transfinite cardinals1874
- Fourier series
- Riemann integral
Made possible
- Hilbert spaces and functional analysis1906-1912
- Dominated convergence theorem1910
- Kolmogorov axioms of probability1933
- signal processing
- quantitative finance