Entropy / CONCEPT
Strong Subadditivity and Conditional Products
Finite Shannon entropy is submodular for three variables, with equality exactly when the last two variables factor conditionally on every active first-coordinate slice.
Closed
DIRECT PREREQUISITES3
DIRECT CONSEQUENCES3
PROOF DEPTH4
DOCUMENT LINKS1
Conditional entropy is subadditive on each slice
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
RELATED KNOWLEDGE
Structural connections
- A finite counterexample to improved thermal recall convergencestructural-affinity · Closed
- Author Information Decompositionstructural-affinity · Closed
- Conditional Choice-Outcome Chain Rulestructural-affinity · Closed
- Conditional Entropy and Its Chain Rulestructural-affinity · Closed
- Conditional Mutual Informationstructural-affinity · Closed
- Conditioning Reduces Entropystructural-affinity · Closed
- Expected Posterior Entropy Reductionstructural-affinity · Closed
- Labelled Responses and Completion Geometrystructural-affinity · Closed
- Markov Data Processingstructural-affinity · Closed
- Mutual Information as an Entropy Balancestructural-affinity · Closed
- Symmetry of Finite Mutual Informationstructural-affinity · Closed
- Vanishing Mutual Information Characterizes Independencestructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
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