Statements (29)
Predicate | Object |
---|---|
gptkbp:instanceOf |
function space
|
gptkbp:alsoKnownAs |
L^p spaces
|
gptkbp:contains |
measurable functions
|
gptkbp:definedIn |
measure space
|
gptkbp:generalizes |
gptkb:Hilbert_space
sequence spaces |
gptkbp:hasDualSpace |
L^q space (where 1/p + 1/q = 1, 1 < p < ∞)
|
gptkbp:heldBy |
gptkb:Hilbert_space
gptkb:Vector complete metric space |
https://www.w3.org/2000/01/rdf-schema#label |
Lebesgue spaces
|
gptkbp:importantFor |
gptkb:interpolation_theory
Fourier analysis partial differential equations Banach space theory |
gptkbp:introducedIn |
early 20th century
|
gptkbp:L^1_space |
integrable functions
|
gptkbp:L^2_space |
gptkb:Hilbert_space
|
gptkbp:L^∞_space |
essentially bounded functions
|
gptkbp:namedAfter |
gptkb:Henri_Lebesgue
|
gptkbp:normedBy |
L^p norm
|
gptkbp:parameter |
p
|
gptkbp:range |
1 ≤ p ≤ ∞
|
gptkbp:usedIn |
gptkb:probability_theory
functional analysis measure theory |
gptkbp:bfsParent |
gptkb:Hardy–Littlewood–Sobolev_inequality
gptkb:Lp_spaces |
gptkbp:bfsLayer |
6
|