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ABC conjectureabstractabstract lang completenessactionadditive combinatoricsadele ringadic valuationaffine groupaffine spacesahiv22ahiv22supportalgebraic geometryalgorithmallow denyallows termalmost orthogonalityalmost periodicityanalysisanalytic number theoryanalytic setangular momentumangular velocityantichain operatorantichain tile countappendapprox hom pfrapproximationarcaritharithmetic geometryarithmetic progressionsas tensorasymptoticsasync runtimeauthorizationauthorizeauthorizerautomata theoryautomorphismauxiliaryball extensionball scalingbase changebase permbasicbasicsbasisbasis linearbatched evaluatorbehavioural theoryberlekamp welchbig opbijectivitybilinear formbindingbirthdaybisimulationbivariateblock rel distancebmobn254borel caratheodorybounding mutualbraketbridgebrownian motionbrun titchmarshbuchi congrbuchi congruencebuchi interbundledbundled semanticscaching logging oraclecaching oraclecadlagcadlag modificationcalculationscampanatocan reach 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Cond multi Dist chain Rule

cond_multiDist_chainRule

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A chain rule for conditional multidistance. Let $\pi:G\to H$ be a homomorphism, and suppose the pairs $(X_i,Y_i)$ are independent across the finite index set. Then $D[X\mid Y]=D[X\mid(\pi X,Y)]+D[\pi X\mid Y]+I\!\left[\sum_iX_i:(\pi X_i)_i\,\middle|\,\left(\pi\!\left(\sum_iX_i\right),(Y_i)_i\right)\right].$ The first term measures the remaining fiberwise multidistance after adjoining each image $\pi(X_i)$ to its conditioning data.