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We investigate converse Marcinkiewicz-Zygmund inequalities on the real line and illustrate how we may use these inequalities to deduce new results on boundedness and mean convergence of Lagrange interpolation. AMS(MOS) Classi cation: 41A10, 42C05

CONVERSE MARCINKIEWICZ-ZYGMUND INEQUALITIES ON THE REAL LINE WITH APPLICATION TO MEAN CONVERGENCE OF LAGRANGE INTERPOLATION