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・ Characterisation (law)
・ Characterisation of pore space in soil
・ Characteristic
・ Characteristic (algebra)
・ Characteristic 2 type
・ Characteristic admittance
・ Characteristic based product configurator
・ Characteristic class
・ Characteristic curve
・ Characteristic energy
・ Characteristic energy length scale
・ Characteristic equation
・ Characteristic equation (calculus)
・ Characteristic exponent
・ Characteristic function
Characteristic function (convex analysis)
・ Characteristic function (probability theory)
・ Characteristic impedance
・ Characteristic length
・ Characteristic mode analysis
・ Characteristic multiplier
・ Characteristic number (fluid dynamics)
・ Characteristic polynomial
・ Characteristic power series
・ Characteristic property
・ Characteristic set
・ Characteristic state function
・ Characteristic subgroup
・ Characteristic time
・ Characteristic variety


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Characteristic function (convex analysis) : ウィキペディア英語版
Characteristic function (convex analysis)

In the field of mathematics known as convex analysis, the characteristic function of a set is a convex function that indicates the membership (or non-membership) of a given element in that set. It is similar to the usual indicator function, and one can freely convert between the two, but the characteristic function as defined below is better-suited to the methods of convex analysis.
==Definition==

Let X be a set, and let A be a subset of X. The characteristic function of A is the function
:\chi_ : X \to \mathbb \cup \
taking values in the extended real number line defined by
:\chi_ (x) := \begin 0, & x \in A; \\ + \infty, & x \not \in A. \end

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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