trureturingGitHub MATHEMATICAL ATLAS

Entropy / CONCEPT

Vanishing Mutual Information Characterizes Independence

Finite classical mutual information in nats vanishes exactly when the joint mass function is the product of its own marginals.

Closed Authored exposition
DIRECT PREREQUISITES2
DIRECT CONSEQUENCES2
PROOF DEPTH3
DOCUMENT LINKS1
THEOREM

Zero mutual information characterizes independence

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Equality in Gibbs' InequalityEquality in Gibbs' InequalityNonnegativity of Finite Classical Mutual InformationNonnegativity of FiniteClassical Mutual InformationVanishing Mutual Information Characterizes IndependenceVanishing Mutual InformationCharacterizes IndependenceThe Finite Mixture Entropy BracketThe Finite Mixture EntropyBracketStrong Subadditivity and Conditional ProductsStrong Subadditivity andConditional Products
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Lean sourceResearch workspace
Status
Closed
Depth
3
Layer
D5/S3
Domain
Entropy
Node ID
D5/S3/Entropy/MutualInformationIndependence
Repository path
D5/S3/Entropy/MutualInformationIndependence.lean
Truth release
sha256:c0d04258d27972c1cf58485e21d64dbcbe336405346ba95133913c64ba2856aa
Source commit
745bf90812f7175f83e1235688249f9495f23bfc
Source tree
143bc6c9ab9054c406f0cdd7f3b296eb38768b5c

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