Statements (28)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:inequality
|
| gptkbp:appliesTo |
convex functions
concave functions |
| gptkbp:category |
Inequalities
|
| gptkbp:field |
gptkb:mathematics
gptkb:probability_theory analysis statistics |
| gptkbp:generalizes |
gptkb:inequality_of_arithmetic_and_geometric_means
|
| https://www.w3.org/2000/01/rdf-schema#label |
Jensen's inequality
|
| gptkbp:introducedIn |
1906
|
| gptkbp:namedAfter |
gptkb:Johan_Jensen
|
| gptkbp:publishedIn |
gptkb:Acta_Mathematica
|
| gptkbp:relatedTo |
gptkb:law_of_large_numbers
gptkb:Holder's_inequality gptkb:Minkowski's_inequality measure theory probability measure expectation convexity |
| gptkbp:statedIn |
f(E[X]) ≤ E[f(X)] for convex f
|
| gptkbp:usedIn |
gptkb:information_theory
gptkb:machine_learning economics optimization |
| gptkbp:bfsParent |
gptkb:Minkowski's_inequality
gptkb:arithmetic-geometric_mean_inequality |
| gptkbp:bfsLayer |
5
|