trureturingGitHub MATHEMATICAL ATLAS

TotalVariation / CONCEPT

Metric Laws and Variational Characterization for Finite Total Variation

Finite total variation satisfies the metric laws, the probability unit bound, and an attained event-gap characterization.

Closed Authored exposition
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES6
PROOF DEPTH3
DOCUMENT LINKS1
THEOREM

Total variation is unconditionally nonnegative

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Finite Total Variation and Pinsker's InequalityFinite Total Variation andPinsker's InequalityMetric Laws and Variational Characterization for Finite Total VariationMetric Laws and VariationalCharacterization for FiniteTotal VariationGreen-Class Window Total VariationGreen-Class Window TotalVariationBounds and Contraction for the Descent DefectBounds and Contraction for theDescent DefectLe Cam's Two-Point Lemma for Every Finite TestLe Cam's Two-Point Lemma forEvery Finite TestBhattacharyya Affinity and the Bretagnolle--Huber BoundBhattacharyya Affinity and theBretagnolle--Huber BoundThe Finite Negentropy BudgetThe Finite Negentropy BudgetProduct Subadditivity of Total VariationProduct Subadditivity of TotalVariation
Proof dependencyStructural affinityDocument link

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Lean sourceResearch workspace
Status
Closed
Depth
3
Layer
D5/S3
Domain
TotalVariation
Node ID
D5/S3/TotalVariation/Metric
Repository path
D5/S3/TotalVariation/Metric.lean
Truth release
sha256:c0d04258d27972c1cf58485e21d64dbcbe336405346ba95133913c64ba2856aa
Source commit
745bf90812f7175f83e1235688249f9495f23bfc
Source tree
143bc6c9ab9054c406f0cdd7f3b296eb38768b5c

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