Statements (19)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Hilbert_space
gptkb:normed_vector_space function space |
| gptkbp:complete |
true
|
| gptkbp:consistsOf |
integrable functions
|
| gptkbp:contains |
all measurable functions f with ∫_X |f| dμ < ∞
|
| gptkbp:definedIn |
measure space (X, μ)
|
| gptkbp:hasDual |
gptkb:L^∞(X,_μ)
|
| gptkbp:hasSubgroup |
L^p(X, μ) for p ≥ 1
|
| https://www.w3.org/2000/01/rdf-schema#label |
L^1(X, μ)
|
| gptkbp:norm |
L^1 norm
|
| gptkbp:normDefinition |
||f||_1 = ∫_X |f| dμ
|
| gptkbp:notation |
L^1
|
| gptkbp:usedIn |
gptkb:probability_theory
functional analysis harmonic analysis measure theory |
| gptkbp:bfsParent |
gptkb:L^1_space
|
| gptkbp:bfsLayer |
6
|