|
gptkbp:instanceOf
|
gptkb:mathematical_concept
|
|
gptkbp:allows
|
Integration of more general functions
|
|
gptkbp:appliesTo
|
Measurable functions
|
|
gptkbp:basisFor
|
gptkb:Lp_spaces
|
|
gptkbp:characterizedBy
|
Integration with respect to a measure
|
|
gptkbp:contrastsWith
|
gptkb:Riemann_integral
|
|
gptkbp:definedIn
|
Measure spaces
Simple functions approximation
|
|
gptkbp:enables
|
gptkb:Dominated_convergence_theorem
gptkb:Fatou's_lemma
gptkb:Fubini's_theorem
gptkb:Monotone_convergence_theorem
|
|
gptkbp:extendsTo
|
gptkb:Riemann_integral
|
|
gptkbp:field
|
gptkb:Mathematics
|
|
gptkbp:generalizes
|
gptkb:Henstock–Kurzweil_integral
gptkb:Lebesgue–Stieltjes_integral
gptkb:Bochner_integral
gptkb:Riemann_integral
gptkb:Pettis_integral
Daniell integral
|
|
gptkbp:hasProperty
|
Linearity
Countable additivity
Monotonicity
Translation invariance
|
|
gptkbp:hasSubfield
|
Measure theory
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
The Lebesgue Integral
|
|
gptkbp:importantFor
|
gptkb:Probability_theory
Functional analysis
Real analysis
|
|
gptkbp:integratesWith
|
Functions not Riemann integrable
Functions with infinite discontinuities
|
|
gptkbp:introducedIn
|
1902
|
|
gptkbp:limitation
|
Not always defined for non-measurable functions
|
|
gptkbp:namedAfter
|
gptkb:Henri_Lebesgue
|
|
gptkbp:relatedTo
|
gptkb:Radon–Nikodym_theorem
Absolute continuity
Lebesgue measure
Integration theory
|
|
gptkbp:requires
|
Measure
Sigma-algebra
|
|
gptkbp:usedFor
|
Integration of functions
|
|
gptkbp:usedIn
|
gptkb:Quantum_mechanics
Fourier analysis
Stochastic processes
Partial differential equations
Probability distributions
|
|
gptkbp:bfsParent
|
gptkb:Sir_John_Charles_Burkill
gptkb:John_Charles_Burkill
|
|
gptkbp:bfsLayer
|
7
|