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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 step function ： ウィキペディア英語版 step function In mathematics, a function on the real numbers is called a step function (or staircase function) if it can be written as a finite linear combination of indicator functions of intervals. Informally speaking, a step function is a piecewise constant function having only finitely many pieces. ==Definition and first consequences== A function $f:\; \backslash mathbb\; \backslash rightarrow\; \backslash mathbb$ is called a step function if it can be written as :$f(x)\; =\; \backslash sum\backslash limits\_^n\; \backslash alpha\_i\; \backslash chi\_(x)\backslash ,$ for all real numbers $x$ where $n\backslash ge\; 0,$ $\backslash alpha\_i$ are real numbers, $A\_i$ are intervals, and $\backslash chi\_A\backslash ,$ (sometimes written as $1\_A$) is the indicator function of $A$: :$\backslash chi\_A(x)\; =\; \backslash begin$ 1 & \mbox x \in A, \\ 0 & \mbox x \notin A. \\ \end In this definition, the intervals $A\_i$ can be assumed to have the following two properties: # The intervals are disjoint, $\backslash scriptstyle\; A\_i\; \backslash ,\backslash cap\backslash ,\; A\_j\; ~=~\; \backslash emptyset$ for $\backslash scriptstyle\; i\; ~\backslash ne~\; j$ # The union of the intervals is the entire real line, $\backslash scriptstyle\; \backslash cup\_^n\; A\_i\; ~=~\; \backslash mathbb\; R.$ Indeed, if that is not the case to start with, a different set of intervals can be picked for which these assumptions hold. For example, the step function :$f\; =\; 4\; \backslash chi\_\; +\; 3\; \backslash chi\_\backslash ,$ can be written as :$f\; =\; 0\backslash chi\_\; +4\; \backslash chi\_\; +7\; \backslash chi\_\; +\; 3\; \backslash chi\_+0\backslash chi\_.\backslash ,$ 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「step function」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.