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gptkbp:instanceOf
|
gptkb:mathematical_concept
|
|
gptkbp:appliesTo
|
measurable functions
|
|
gptkbp:basisFor
|
gptkb:probability_theory
functional analysis
L^p spaces
modern analysis
|
|
gptkbp:category
|
integration
mathematical analysis
|
|
gptkbp:contrastsWith
|
gptkb:Riemann_integration
|
|
gptkbp:definedIn
|
measurable sets
|
|
gptkbp:enables
|
gptkb:Tonelli's_theorem
gptkb:Fubini's_theorem
gptkb:Dominated_Convergence_Theorem
gptkb:Monotone_Convergence_Theorem
integration of more general functions
convergence theorems
|
|
gptkbp:field
|
gptkb:mathematics
measure theory
real analysis
|
|
gptkbp:generalizes
|
gptkb:Riemann_integration
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Lebesgue integration
|
|
gptkbp:introducedIn
|
1902
|
|
gptkbp:namedAfter
|
gptkb:Henri_Lebesgue
|
|
gptkbp:relatedTo
|
gptkb:Borel_sets
gptkb:Radon–Nikodym_theorem
Lebesgue measure
integration theory
improper integrals
signed measures
absolute continuity
complex measures
non-negative functions
simple functions
|
|
gptkbp:requires
|
measure space
|
|
gptkbp:usedFor
|
integration of functions
|
|
gptkbp:uses
|
sigma-algebra
measure
|
|
gptkbp:bfsParent
|
gptkb:The_Theory_of_Integration
gptkb:Lp_space
gptkb:Fatou's_lemma
gptkb:Henri_Lebesgue
gptkb:Monotone_convergence_theorem
|
|
gptkbp:bfsLayer
|
6
|