Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
function space
|
| gptkbp:closed |
addition
scalar multiplication |
| gptkbp:compatibleWith |
necessarily bounded
necessarily continuous |
| gptkbp:contains |
all functions with compact support
|
| gptkbp:definedIn |
measure space
|
| gptkbp:dualSpaceOf |
L^∞ functions
|
| gptkbp:example |
f(x) = e^{-x^2} on R
|
| gptkbp:form |
gptkb:Hilbert_space
|
| gptkbp:hasSubgroup |
measurable functions
|
| https://www.w3.org/2000/01/rdf-schema#label |
L^1 functions
|
| gptkbp:importantFor |
complete normed vector space
|
| gptkbp:integrableWithRespectTo |
absolute value
|
| gptkbp:L^1_norm |
integral of absolute value
|
| gptkbp:norm |
L^1 norm
|
| gptkbp:notation |
gptkb:L^1(X,_μ)
|
| gptkbp:requires |
integral of |f| is finite
|
| gptkbp:usedIn |
gptkb:probability_theory
Fourier analysis functional analysis |
| gptkbp:bfsParent |
gptkb:Riemann–Lebesgue_lemma
|
| gptkbp:bfsLayer |
6
|