trureturingGitHub MATHEMATICAL ATLAS

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 Authored exposition
DIRECT PREREQUISITES3
DIRECT CONSEQUENCES2
PROOF DEPTH4
DOCUMENT LINKS1
THEOREM

Conditional entropy is subadditive on each slice

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Conditional Entropy and Its Chain RuleConditional Entropy and ItsChain RuleMutual Information as an Entropy BalanceMutual Information as anEntropy BalanceVanishing Mutual Information Characterizes IndependenceVanishing Mutual InformationCharacterizes IndependenceStrong Subadditivity and Conditional ProductsStrong Subadditivity andConditional ProductsConditional Choice-Outcome Chain RuleConditional Choice-OutcomeChain RuleConditional Mutual InformationConditional Mutual Information
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Lean sourceResearch workspace
Status
Closed
Depth
4
Layer
D5/S3
Domain
Entropy
Node ID
D5/S3/Entropy/Submodularity/StrongSubadditivity
Repository path
D5/S3/Entropy/Submodularity/StrongSubadditivity.lean
Truth release
sha256:c0d04258d27972c1cf58485e21d64dbcbe336405346ba95133913c64ba2856aa
Source commit
745bf90812f7175f83e1235688249f9495f23bfc
Source tree
143bc6c9ab9054c406f0cdd7f3b296eb38768b5c

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