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Copula.Order.SymmetricSchur

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Schur comparison in both coordinate directions #

This distinguishes the paper's two-direction comparison from the directional SchurLE used for Chatterjee's xi.

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def ProbabilityTheory.Copula.SchurBothLE (C D : Copula 2) :
Prop

Schur comparison of both conditional distributions.

Equations
Instances For
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    theorem ProbabilityTheory.Copula.SchurBothLE.refl (C : Copula 2) :
    C.SchurBothLE C
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    theorem ProbabilityTheory.Copula.SchurBothLE.trans {C D E : Copula 2} (h : C.SchurBothLE D) (k : D.SchurBothLE E) :
    C.SchurBothLE E
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    @[simp]
    theorem ProbabilityTheory.Copula.schurBothLE_transpose_iff (C D : Copula 2) :
    C.transpose.SchurBothLE D.transpose ↔ C.SchurBothLE D
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    theorem ProbabilityTheory.Copula.schurBothLE_iff_of_exchangeable {C D : Copula 2} (hC : C.IsExchangeable) (hD : D.IsExchangeable) :
    C.SchurBothLE D ↔ C.SchurLE D
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    theorem ProbabilityTheory.Copula.schurBothLE_iff_of_archimedean {C D : Copula 2} (hC : C.IsArchimedean) (hD : D.IsArchimedean) :
    C.SchurBothLE D ↔ C.SchurLE D