Entropy / CONCEPT
Mutual Information Vanishes on Product Laws
Finite classical mutual information in nats vanishes on every normalized product mass function.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES0
PROOF DEPTH3
DOCUMENT LINKS1
Mutual information vanishes on product laws
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
None recorded in this release.
RELATED KNOWLEDGE
Structural connections
- Conditional Entropy and Its Chain Rulestructural-affinity · Closed
- Conditioning Reduces Entropystructural-affinity · Closed
- Marginal Monotonicity of Finite Classical KL Divergencestructural-affinity · Closed
- Mutual Information as an Entropy Balancestructural-affinity · Closed
- Nonnegativity of Finite Classical Mutual Informationstructural-affinity · Closed
- Symmetry of Finite Mutual Informationstructural-affinity · Closed
- The Feedback Divergence Identitystructural-affinity · Closed
- Vanishing Mutual Information Characterizes Independencestructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
Content history
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