Divergence / CONCEPT
The Grandmother Theorem
Absolutely continuous finite mass functions have nonnegative Kullback-Leibler divergence.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES13
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
- Finite-History Soft Controltruth-dependency · Closed
- Marginal Monotonicity of Finite Classical KL Divergencetruth-dependency · Closed
- Maximum Entropy on a Finite Alphabettruth-dependency · Closed
- Model-level equivalence does not imply measure-level equivalencetruth-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
- Classical Data Processing as a Chain Identitystructural-affinity · Closed
- Classical Data Processing on General Supportstructural-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
- Finite-History Soft Controlstructural-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
- Model-level equivalence does not imply measure-level equivalencestructural-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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