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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
sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
Source commit
b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
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37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

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