Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Hilbert_space
function space |
| gptkbp:basisFor |
orthonormal basis exists
|
| gptkbp:complete |
true
|
| gptkbp:contains |
square-integrable functions
|
| gptkbp:containsElement |
equivalence classes of measurable functions
|
| gptkbp:definedIn |
measure space (X, μ)
|
| gptkbp:hasDual |
itself (self-dual)
|
| gptkbp:hasSubgroup |
L^1(X, μ) (if μ is finite)
|
| https://www.w3.org/2000/01/rdf-schema#label |
L^2(X, μ)
|
| gptkbp:innerProduct |
integral of product of functions
|
| gptkbp:isBanachSpace |
true
|
| gptkbp:isVectorSpace |
true
|
| gptkbp:namedAfter |
gptkb:Lebesgue
|
| gptkbp:norm |
gptkb:L^2-norm
|
| gptkbp:notation |
gptkb:L^2-space
|
| gptkbp:separates |
true (if X is σ-finite)
|
| gptkbp:usedIn |
gptkb:probability_theory
gptkb:signal_processing functional analysis quantum mechanics |
| gptkbp:bfsParent |
gptkb:Lebesgue_space_L2
gptkb:L^2_space |
| gptkbp:bfsLayer |
6
|