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This paper investigates the optimal recovery of Sobolev spaces Wr1[-1,1],r ∈ N in the space L1[-1,1].They obtain the values of the sampling numbers of Wr1[-1,1]in L1[-1,1]and show that the Lagrange interpolation algorithms based on the extreme points of Chebyshev polynomials are optimal algorithms.Meanwhile,they prove that the extreme points of Chebyshev polynomials are optimal Lagrange interpolation nodes.