Statements (20)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:inequality
|
| gptkbp:appliesTo |
gptkb:n-dimensional_Euclidean_space
|
| gptkbp:field |
gptkb:geometry
gptkb:mathematics analysis |
| gptkbp:form |
|A|^{n-1} ≤ ∏_{i=1}^n |π_i(A)|, where π_i(A) is the projection onto the i-th coordinate hyperplane.
|
| gptkbp:generalizes |
isoperimetric inequality
|
| https://www.w3.org/2000/01/rdf-schema#label |
Loomis-Whitney inequality
|
| gptkbp:namedAfter |
gptkb:Hassler_Whitney
gptkb:Lynn_Harold_Loomis |
| gptkbp:publicationYear |
1949
|
| gptkbp:publishedIn |
gptkb:Bulletin_of_the_American_Mathematical_Society
|
| gptkbp:relatedTo |
gptkb:Holder's_inequality
Brunn-Minkowski inequality |
| gptkbp:state |
The volume of a subset of n-dimensional space is bounded by the product of the volumes of its projections onto the coordinate hyperplanes.
|
| gptkbp:usedIn |
analysis
combinatorics geometric measure theory |
| gptkbp:bfsParent |
gptkb:Larry_Loomis
|
| gptkbp:bfsLayer |
8
|