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The resulting discrepancy is the classical energy distance $$\\mathcal E_q^2(\\mu, \\omega) = -\\frac{1}{2}\\iint_{\\mathbb{R}^d \\times \\mathbb{R}^d} |x-y|^q \\, d(\\mu - \\omega)(x)\\, d(\\mu - \\omega)(y),$$ and we ask how fast the best $N$-point empirical approximation $\\inf_{\\mu_N \\in \\mathcal{P}^N}\\mathcal{E}_q(\\mu_N,\\omega)$ decays as $N \\to \\infty$. 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The resulting discrepancy is the classical energy distance $$\\mathcal E_q^2(\\mu, \\omega) = -\\frac{1}{2}\\iint_{\\mathbb{R}^d \\times \\mathbb{R}^d} |x-y|^q \\, d(\\mu - \\omega)(x)\\, d(\\mu - \\omega)(y),$$ and we ask how fast the best $N$-point empirical approximation $\\inf_{\\mu_N \\in \\mathcal{P}^N}\\mathcal{E}_q(\\mu_N,\\omega)$ decays as $N \\to \\infty$. 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