Entropy / CONCEPT
Equality at the Lower Endpoint of Conditional Entropy
Vanishing finite conditional entropy in nats characterizes point-mass conditional laws exactly on nonzero-marginal slices.
Closed
DIRECT PREREQUISITES2
DIRECT CONSEQUENCES5
PROOF DEPTH5
DOCUMENT LINKS1
Point-mass conditionals on the marginal support force zero entropy
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
- Commitment Information Upper Boundtruth-dependency · Closed
- Equality and Strict Loss under Deterministic Forgettingtruth-dependency · Closed
- Equality in the Upper Mixture-Entropy Boundtruth-dependency · Closed
- Information Cost of Concept Completiontruth-dependency · Closed
- Prediction Stability from Zero Conditional Entropytruth-dependency · Closed
RELATED KNOWLEDGE
Structural connections
- Commitment Information Upper Boundstructural-affinity · Closed
- Deterministic Output Entropy Ratestructural-affinity · Closed
- Equality and Strict Loss under Deterministic Forgettingstructural-affinity · Closed
- Equality Cases for Finite Shannon Entropystructural-affinity · Closed
- Equality in the Green-Class Window Entropy Boundstructural-affinity · Closed
- Equality in the Upper Mixture-Entropy Boundstructural-affinity · Closed
- Information Cost of Concept Completionstructural-affinity · Closed
- Itinerary Completionstructural-affinity · Closed
- Nonnegativity of Finite Entropystructural-affinity · Closed
- Prediction Stability from Zero Conditional Entropystructural-affinity · Closed
- The Entropy-Divergence Consistency Identitystructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
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