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We investigate polarized deuteron structure functions at small values of the Bjorken variable, x < 0.1. In this region contributions from the coherent interaction of diffractively excited hadronic states with both nucleons become important. A proper treatment of this process requires an extension of the Glauber-Gribov multiple scattering theory to include spin degrees of freedom. In the kinematic domain of current fixed target experiments we observe that shadowing effects in g_1d are approximately twice as large as for the unpolarized structure function F_2d. Furthermore at x < 0.1 the tensor structure function b_1 is found to receive significant contributions from coherent double scattering.

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