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In this paper, we mainly investigate the average sampling problem for the homogeneous random fields in a reproducing kernel subspace of mixed Lebesgue space. Based on the counterpart sampling result for the deterministic signals in the same space, a mean square convergence result for recovering the homogeneous random fields by the iterative reconstruction algorithm is obtained.

Average sampling theorem for the homogeneous random fields in a reproducing kernel subspace of mixed Lebesgue space