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Additional resources for Dri Dietary Reference Intakes for Vitamin A, Vitamin K, Arsenic, Boron, Chromium, Copper, Iodine, Iron, Manganese, Molybdenum, Nickel, Silicon, vanadi: Um, and Zinc

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296). We assume that this is the case. Then Eµ (gn log+ gn ) ≤ Eµ (gn+1 log+ gn+1 ), n = 1, 2, · · · , so that limn→∞ Eµ (gn log+ gn ) exists, which may be finite or infinite. We assume that this limit is finite, say c. e. Moreover by Fatou’s lemma, Eµ (g log g) ≤ c. ∞ Assume that the sequence (gn )n=1 is uniformly integrable so that this sequence together with g forms a martingale. From martingale theory ([4], + p. 296) the sequence (gn log+ gn )∞ n=1 together with the function g log g is a submartingale of non-negative functions, so, again from martingale theory ([4], p.

Then the set of all p for which F (p) is the minimum value of F on M is called the Fr´echet Mean set of Q, denoted by CQ . If this set is a singleton, say {µF }, then µF is called the Fr´echet Mean of Q. If X1 , X2 , . . , Xn are independent and identically distributed (iid) M-valued random variables defined on some proba. bility space (Ω, F , P ) with common distribution Q, and Qn = n1 nj=1 δXj is the corresponding empirical distribution, then the Fr´echet mean set of Qn is called the sample Fr´echet mean set, denoted by CQn .

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Dri Dietary Reference Intakes for Vitamin A, Vitamin K, Arsenic, Boron, Chromium, Copper, Iodine, Iron, Manganese, Molybdenum, Nickel, Silicon, vanadi: Um, and Zinc by Iom


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