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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Subadditivity ： ウィキペディア英語版 Subadditivity In mathematics, subadditivity is a property of a function that states, roughly, that evaluating the function for the sum of two elements of the domain always returns something less than or equal to the sum of the function's values at each element. There are numerous examples of subadditive functions in various areas of mathematics, particularly norms and square roots. Additive maps are special cases of subadditive functions. ==Definitions== A subadditive function is a function $f\; \backslash colon\; A\; \backslash to\; B$, having a domain ''A'' and an ordered codomain ''B'' that are both closed under addition, with the following property: ::$\backslash forall\; x,\; y\; \backslash in\; A,\; f(x+y)\backslash leq\; f(x)+f(y).$ An example is the square root function, having the non-negative real numbers as domain and codomain, since $\backslash forall\; x,\; y\; \backslash geq\; 0$ we have: ::$\backslash sqrt\backslash leq\; \backslash sqrt+\backslash sqrt.$ A sequence $\backslash left\; \backslash ,\; n\; \backslash geq\; 1$, is called subadditive if it satisfies the inequality ::$(1)\; \backslash qquad\; a\_\backslash leq\; a\_n+a\_m$ for all ''m'' and ''n''. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Subadditivity」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.