trureturingGitHub MATHEMATICAL ATLAS

Entropy / CONCEPT

The Finite Mixture Entropy Bracket

Finite mixture entropy lies between weighted component entropy and that entropy plus the weight entropy; the upper equality case for pairwise disjoint supports is not covered in this stratum.

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DIRECT PREREQUISITES4
DIRECT CONSEQUENCES1
PROOF DEPTH5
DOCUMENT LINKS1
THEOREM

The first mixture-joint marginal is the weight law

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Conditioning Reduces EntropyConditioning Reduces EntropyNonnegativity of Finite EntropyNonnegativity of Finite EntropyVanishing Mutual Information Characterizes IndependenceVanishing Mutual InformationCharacterizes IndependenceSymmetry of Finite Mutual InformationSymmetry of Finite MutualInformationThe Finite Mixture Entropy BracketThe Finite Mixture EntropyBracketEquality in the Upper Mixture-Entropy BoundEquality in the Upper Mixture-Entropy Bound
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Lean sourceResearch workspace
Status
Closed
Depth
5
Layer
D5/S3
Domain
Entropy
Node ID
D5/S3/Entropy/Mixing/MixtureEntropyBracket
Repository path
D5/S3/Entropy/Mixing/MixtureEntropyBracket.lean
Truth release
sha256:c0d04258d27972c1cf58485e21d64dbcbe336405346ba95133913c64ba2856aa
Source commit
745bf90812f7175f83e1235688249f9495f23bfc
Source tree
143bc6c9ab9054c406f0cdd7f3b296eb38768b5c

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