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.

Let ${\displaystyle X}$ be a set, and let ${\displaystyle A}$ be a subset of ${\displaystyle X}$. The characteristic function of ${\displaystyle A}$ is the function

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