Statements (31)
Predicate | Object |
---|---|
gptkbp:instanceOf |
gptkb:mathematical_concept
function space |
gptkbp:alsoKnownAs |
gptkb:Lebesgue_space
|
gptkbp:complete |
true
|
gptkbp:containsElement |
sequence (x_n) with sum |x_n|^p < ∞
|
gptkbp:definedIn |
1 ≤ p ≤ ∞
|
gptkbp:field |
gptkb:mathematics
functional analysis |
gptkbp:generalizes |
gptkb:l^∞_space
gptkb:l^1_space gptkb:l^2_space |
gptkbp:hasDual |
l^q space (where 1/p + 1/q = 1, 1 < p < ∞)
|
gptkbp:hasNorm |
p-norm
|
gptkbp:hasSpecialCase |
l^2 space is Hilbert space
|
gptkbp:hasSubgroup |
gptkb:Hilbert_space
gptkb:normed_vector_space sequence space |
https://www.w3.org/2000/01/rdf-schema#label |
l^p space
|
gptkbp:namedAfter |
gptkb:Lebesgue
|
gptkbp:notation |
l^p
ℓ^p |
gptkbp:relatedTo |
Lp space (function spaces)
|
gptkbp:separates |
false (for p = ∞)
true (for 1 ≤ p < ∞) |
gptkbp:usedIn |
gptkb:machine_learning
gptkb:probability_theory gptkb:signal_processing analysis statistics |
gptkbp:bfsParent |
gptkb:Hilbert_space
|
gptkbp:bfsLayer |
4
|