Statements (31)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
gptkb: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 gptkb:sequence_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:analysis
gptkb:machine_learning gptkb:probability_theory gptkb:signal_processing statistics |
| gptkbp:bfsParent |
gptkb:Sequence_space
|
| gptkbp:bfsLayer |
9
|
| https://www.w3.org/2000/01/rdf-schema#label |
l^p space
|