trureturingGitHub MATHEMATICAL ATLAS

Entropy / CONCEPT

Equality Cases for Finite Shannon Entropy

The two endpoints of the finite Shannon-entropy bracket in nats characterize the uniform law and point masses.

Closed Authored exposition
DIRECT PREREQUISITES2
DIRECT CONSEQUENCES4
PROOF DEPTH4
DOCUMENT LINKS1
THEOREM

Maximum entropy characterizes the uniform law

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Equality in Gibbs' InequalityEquality in Gibbs' InequalityThe Entropy-Divergence Consistency IdentityThe Entropy-DivergenceConsistency IdentityEquality Cases for Finite Shannon EntropyEquality Cases for FiniteShannon EntropyEquality at the Lower Endpoint of Conditional EntropyEquality at the Lower Endpointof Conditional EntropyEquality in the Green-Class Window Entropy BoundEquality in the Green-ClassWindow Entropy BoundEstimator-Error Lower Bounds from Finite Fano InequalitiesEstimator-Error Lower Boundsfrom Finite Fano InequalitiesBinary Character Uniform Information ExactnessBinary Character UniformInformation Exactness
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Lean sourceResearch workspace
Status
Closed
Depth
4
Layer
D5/S3
Domain
Entropy
Node ID
D5/S3/Entropy/EntropyEquality
Repository path
D5/S3/Entropy/EntropyEquality.lean
Truth release
sha256:c0d04258d27972c1cf58485e21d64dbcbe336405346ba95133913c64ba2856aa
Source commit
745bf90812f7175f83e1235688249f9495f23bfc
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143bc6c9ab9054c406f0cdd7f3b296eb38768b5c

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