We measure a sign interlacing phenomenon for Bessel sequences (uk) in L2 spaces terms of the Kantorovich–Rubinstein mass moving norm ‖uk‖KR. Our main observation shows that, quantitatively, rate at which ‖uk‖KR→0 heavily depends on Bernstein–Kolmogorov widths compact set Lipschitz functions. In particular, it dimension space. also establish lower bound convergence norms ‖uk‖X→0 basis/frame any ...