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{\\int_{\\mathbb{T}^{d}}}\\left( \\frac{1}{H} {\\int_{R}^{R+H}}\\left\\vert \\sum_{k\\in\\mathbb{Z}^{d}}\\chi _{r\\Omega-x}(k)-r^{d}\\left\\vert \\Omega\\right\\vert \\right\\vert^{2}dr\\right)^{p/2}dx\\right\\} ^{1/p}. $ We obtain estimates for fixed values of $H$ and $R\\to\\infty$, and also asymptotic estimates when 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