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Entropy / CONCEPT

Shannon Entropy Is Invariant Under Injective Relabeling

Discrete Shannon entropy is invariant under injective relabeling of the support.

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DIRECT PREREQUISITES1
DIRECT CONSEQUENCES5
PROOF DEPTH3
DOCUMENT LINKS1
THEOREM

Shannon entropy is unchanged by injective relabeling

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Maximum Entropy on a Finite AlphabetMaximum Entropy on a FiniteAlphabetShannon Entropy Is Invariant Under Injective RelabelingShannon Entropy Is InvariantUnder Injective RelabelingEquality and Strict Loss under Deterministic ForgettingEquality and Strict Loss underDeterministic ForgettingFusion State EntropyFusion State EntropyObservation-Word and Completion Information DecompositionObservation-Word and CompletionInformation DecompositionMulti-Target Information ChainMulti-Target Information ChainDifferential Entropy Change of VariablesDifferential Entropy Change ofVariables
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Lean sourceResearch workspace
Status
Closed
Depth
3
Layer
D5/S3
Domain
Entropy
Node ID
D5/S3/Entropy/Relabeling/InjectiveInvariance
Repository path
D5/S3/Entropy/Relabeling/InjectiveInvariance.lean
Truth release
sha256:c0d04258d27972c1cf58485e21d64dbcbe336405346ba95133913c64ba2856aa
Source commit
745bf90812f7175f83e1235688249f9495f23bfc
Source tree
143bc6c9ab9054c406f0cdd7f3b296eb38768b5c

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