Statements (28)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:application |
gptkb:probability_theory
optimization geometry of Banach spaces |
| gptkbp:definedIn |
set of points with fixed Lp norm
|
| gptkbp:dimensions |
n-1
|
| gptkbp:field |
gptkb:mathematics
|
| gptkbp:hasSpecialCase |
Euclidean sphere (when p=2)
cube surface (when p=∞) taxicab sphere (when p=1) unit sphere (when norm = 1) |
| gptkbp:hasSubfield |
functional analysis
|
| https://www.w3.org/2000/01/rdf-schema#label |
Lp sphere
|
| gptkbp:notation |
S_p
S_p^n |
| gptkbp:parameter |
n
p |
| gptkbp:property |
compact
boundary of Lp ball centrally symmetric convex for p ≥ 1 smooth for p > 1 |
| gptkbp:relatedTo |
gptkb:normed_vector_space
gptkb:Lp_space gptkb:Minkowski_functional unit ball |
| gptkbp:bfsParent |
gptkb:Lp_ball
|
| gptkbp:bfsLayer |
6
|