Statements (28)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
Lebesgue square-integrable function spaces
|
| gptkbp:basisFor |
orthonormal basis
|
| gptkbp:complete |
yes
|
| gptkbp:consistsOf |
measurable functions
|
| gptkbp:definedIn |
measure space
|
| gptkbp:example |
L2(R)
L2([0,1]) |
| gptkbp:hasDual |
itself (self-dual)
|
| gptkbp:hasSubgroup |
gptkb:Lp_spaces
|
| gptkbp:heldBy |
gptkb:Hilbert_space
|
| https://www.w3.org/2000/01/rdf-schema#label |
L2 spaces
|
| gptkbp:importantFor |
gptkb:signal_processing
functional analysis quantum mechanics statistics |
| gptkbp:innerProduct |
∫f(x)g(x) dμ(x)
|
| gptkbp:namedAfter |
gptkb:Henri_Lebesgue
|
| gptkbp:norm |
L2 norm
|
| gptkbp:normFormula |
(∫|f|^2 dμ)^{1/2}
|
| gptkbp:property |
functions whose square is Lebesgue integrable
|
| gptkbp:separates |
yes
|
| gptkbp:usedFor |
gptkb:machine_learning
gptkb:probability_theory gptkb:PDEs Fourier analysis |
| gptkbp:bfsParent |
gptkb:Hilbert_space_theory
|
| gptkbp:bfsLayer |
7
|