Faddeev’s axioms
E45254
Faddeev’s axioms are a set of conditions characterizing Shannon entropy in information theory, providing an alternative but equivalent axiomatization to the Shannon–Khinchin framework.
Statements (30)
| Predicate | Object |
|---|---|
| instanceOf |
axiomatization of entropy
ⓘ
characterization of Shannon entropy ⓘ set of axioms in information theory ⓘ |
| appliesTo | finite discrete probability distributions ⓘ |
| assumes | entropy is a real-valued function on discrete probability distributions ⓘ |
| characterizes | Shannon entropy ⓘ |
| clarifies | why Shannon entropy has its specific functional form ⓘ |
| field | information theory ⓘ |
| implies | Shannon entropy is the unique solution up to scale ⓘ |
| includesCondition |
continuity of entropy
ⓘ
normalization condition for entropy ⓘ recursivity (grouping) condition ⓘ symmetry of entropy under permutation of outcomes ⓘ |
| influenced | later axiomatizations of entropy and information measures ⓘ |
| isAlternativeTo | Shannon–Khinchin axioms ⓘ |
| isEquivalentTo | Shannon–Khinchin axioms ⓘ |
| mainGoal | uniquely characterize Shannon entropy up to a positive multiplicative constant ⓘ |
| mathematicalDomain |
functional equations
ⓘ
probability theory ⓘ |
| namedAfter | Dmitry Faddeev ⓘ |
| relatedTo |
Shannon entropy
ⓘ
Shannon–Khinchin axioms ⓘ characterization theorems for entropy ⓘ |
| requires | entropy of a certain two-point distribution to be positive ⓘ |
| supports | uniqueness of Shannon entropy under natural requirements ⓘ |
| typeOfCondition | axiomatic characterization ⓘ |
| usedFor |
foundations of information theory
ⓘ
justification of Shannon entropy ⓘ |
| usesConcept |
information measure
ⓘ
probability distribution ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.