A complement to the Chebyshev integral inequality

Statistics & Probability Letters 168:108934. Theorem 1.2 gives the exact equality case for monotone covariance: Cov(f(X),g(X))=0 iff f(X) or g(X) is a.s. constant. The proof uses the independent-copy product identity appearing conditionally in DS17. This supports that equality step, not the later quantizer-cell or nuisance-rank conclusions.