Statements (29)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Hilbert_space
function space |
| gptkbp:alsoKnownAs |
essentially bounded functions space
|
| gptkbp:category |
gptkb:mathematics
analysis |
| gptkbp:complete |
true
|
| gptkbp:contains |
essentially bounded measurable functions
|
| gptkbp:definedIn |
measure space
|
| gptkbp:dualPolyhedron |
gptkb:L^1_space
|
| gptkbp:generalizes |
bounded functions
|
| gptkbp:hasSubgroup |
measurable functions
|
| https://www.w3.org/2000/01/rdf-schema#label |
L^∞ space
|
| gptkbp:introduced |
gptkb:Frigyes_Riesz
|
| gptkbp:norm |
essential supremum norm
|
| gptkbp:notation |
gptkb:L^∞(X,_μ)
|
| gptkbp:property |
gptkb:normed_vector_space
contains equivalence classes of functions dual space of L^1 norm is defined almost everywhere not reflexive unit ball is compact in weak* topology unit ball is not compact in norm topology separable if and only if measure space is purely atomic and countable |
| gptkbp:relatedTo |
L^p spaces
|
| gptkbp:usedIn |
gptkb:probability_theory
functional analysis measure theory |
| gptkbp:bfsParent |
gptkb:L^p_space
|
| gptkbp:bfsLayer |
5
|