Effective domain  In convex analysis, a branch of mathematics, the effective domain is an extension of the domain of a function. Given a vector space "X" then a convex function mapping to the extended reals, formula_1, has an "effective domain" defined by If the function is concave, then the "effective domain" is  The effective domain is equivalent to the projection of the epigraph of a function formula_1 onto "X". That is  Note that if a convex function is mapping to the normal real number line given by formula_6 then the effective domain is the same as the normal definition of the domain. A function formula_1 is a proper convex function if and only if "f" is convex, the effective domain of "f" is nonempty and formula_8 for every formula_9.