Divergence / CONCEPT
Equality in Gibbs' Inequality
Equality in finite Gibbs' inequality characterizes identical probability distributions.
Closed
DIRECT PREREQUISITES2
DIRECT CONSEQUENCES6
PROOF DEPTH2
DOCUMENT LINKS1
Zero relative entropy characterizes equal distributions
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
- Equality Cases for Finite Shannon Entropytruth-dependency · Closed
- Strict Positivity of Finite Classical KL Divergencetruth-dependency · Closed
- The Classical Petz Equality Conditiontruth-dependency · Closed
- Vanishing Mutual Information Characterizes Independencetruth-dependency · Closed
- When the General-Support Data-Processing Defect Vanishestruth-dependency · Closed
- Zero Characterization of Finite Renyi Divergencetruth-dependency · Closed
RELATED KNOWLEDGE
Structural connections
- Bayesian Reverse Recovery at Zero DPI Defectstructural-affinity · Closed
- Channel Monotonicity of Finite Classical KL Divergencestructural-affinity · Closed
- Classical Data Processing as a Chain Identitystructural-affinity · Closed
- Equality Cases for Finite Shannon Entropystructural-affinity · Closed
- Equality in the Finite Log-Sum Inequalitystructural-affinity · Closed
- Marginal Monotonicity of Finite Classical KL Divergencestructural-affinity · Closed
- Nonnegativity of the Classical Data-Processing Defectstructural-affinity · Closed
- Strict Positivity of Finite Classical KL Divergencestructural-affinity · Closed
- Strict Positivity of the Classical Data-Processing Defectstructural-affinity · Closed
- The Classical Petz Equality Conditionstructural-affinity · Closed
- The Data-Processing Defect on General Supportstructural-affinity · Closed
- The Entropy-Divergence Consistency Identitystructural-affinity · Closed
- The Grandmother Theoremstructural-affinity · Closed
- Vanishing Mutual Information Characterizes Independencestructural-affinity · Closed
- When the General-Support Data-Processing Defect Vanishesstructural-affinity · Closed
- Zero Characterization of Finite Renyi Divergencestructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
Content history
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