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gptkbp:instanceOf
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gptkb:mathematical_concept
|
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gptkbp:appliesTo
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measurable functions
|
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gptkbp:basisFor
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L^p spaces
|
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gptkbp:contrastsWith
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gptkb:Riemann–Stieltjes_integral
|
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gptkbp:definedIn
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measure spaces
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gptkbp:enables
|
interchange of limits and integrals under certain conditions
integration of functions with respect to arbitrary measures
integration of more general functions
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gptkbp:field
|
gptkb:mathematics
measure theory
real analysis
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gptkbp:generalizes
|
gptkb:Riemann_integral
|
|
https://www.w3.org/2000/01/rdf-schema#label
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Lebesgue integral
|
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gptkbp:importantFor
|
gptkb:probability_theory
functional analysis
|
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gptkbp:introducedIn
|
1902
|
|
gptkbp:namedAfter
|
gptkb:Henri_Lebesgue
|
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gptkbp:notation
|
∫ f dμ
∫ f(x) dμ(x)
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gptkbp:relatedTo
|
gptkb:Dominated_convergence_theorem
gptkb:Fatou's_lemma
gptkb:Fubini's_theorem
gptkb:Monotone_convergence_theorem
gptkb:Radon–Nikodym_theorem
Lebesgue measure
|
|
gptkbp:usedFor
|
integration of functions
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|
gptkbp:usedIn
|
Fourier analysis
ergodic theory
modern analysis
probability spaces
|
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gptkbp:bfsParent
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gptkb:Measure_Theory
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gptkbp:bfsLayer
|
5
|