Divergence / CONCEPT
The Grandmother Theorem
Absolutely continuous finite mass functions have nonnegative Kullback-Leibler divergence.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES11
PROOF DEPTH1
DOCUMENT LINKS1
Absolutely continuous finite masses have nonnegative KL divergence
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
- Entropy Production by Coherence Deletiontruth-dependency · Closed
- Equality in Gibbs' Inequalitytruth-dependency · Closed
- Finite Fano with an Arbitrary Observation Referencetruth-dependency · Closed
- Finite Total Variation and Pinsker's Inequalitytruth-dependency · Closed
- Marginal Monotonicity of Finite Classical KL Divergencetruth-dependency · Closed
- Maximum Entropy on a Finite Alphabettruth-dependency · Closed
- Nonnegativity of Finite Classical Mutual Informationtruth-dependency · Closed
- Nonnegativity of the Classical Data-Processing Defecttruth-dependency · Closed
- Strict Positivity of Finite Classical KL Divergencetruth-dependency · Closed
- The Classical Petz Equality Conditiontruth-dependency · Closed
- The Data-Processing Defect on General Supporttruth-dependency · Closed
RELATED KNOWLEDGE
Structural connections
- Chain Rule for Finite Classical KL Divergencestructural-affinity · Closed
- Classical Data Processing as a Chain Identitystructural-affinity · Closed
- Classical Data Processing on General Supportstructural-affinity · Closed
- Entropy Production by Coherence Deletionstructural-affinity · Closed
- Equality in Gibbs' Inequalitystructural-affinity · Closed
- Equality in the Finite Log-Sum Inequalitystructural-affinity · Closed
- Finite Fano with an Arbitrary Observation Referencestructural-affinity · Closed
- Finite Total Variation and Pinsker's Inequalitystructural-affinity · Closed
- Log-Sum Inequality and Joint Convexity on General Supportstructural-affinity · Closed
- Marginal Monotonicity of Finite Classical KL Divergencestructural-affinity · Closed
- Maximum Entropy on a Finite Alphabetstructural-affinity · Closed
- Nonnegativity of Finite Classical Mutual Informationstructural-affinity · Closed
- Nonnegativity of the Classical Data-Processing Defectstructural-affinity · Closed
- Product Additivity of Finite Classical KL Divergencestructural-affinity · Closed
- Strict Positivity of Finite Classical KL Divergencestructural-affinity · Closed
- The Classical Petz Equality Conditionstructural-affinity · Closed
- The Data-Processing Defect on General Supportstructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
Content history
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