Binary mekso operator: uniform probability A(X2)u(X for input (X1,X where X1 is a number and X2 is a set or space. (See notes for details).
Establish (elsewhere) a universal set/topological space O and equip it with a measure L; then X1 must be an element of O, and X2 must be a subset/subspace of O and will be equipped with/inherit the same measure L (restricted to it) and the appropriate topology. Let Y be the maximal non-discrete subset/subspace of X2 (in other words, all non-discrete subsets/subspaces of X2 are subsets/subspaces of Y). The term 'A' in the definition is a nonnegative-valued 'function' which is defined on the category of sets; it produces the proper normalization (by being the reciprocal of the integral of u over O with respect to L iff such is well-defined and finite and positive; otherwise, it is identically 0). The term 'u' in the definition is defined to be the sum of the indicator function (Kronecker delta) for Y (outputting 1 iff X1 is an element Y, and outputting 0 otherwise) and the Dirac delta of: 1 minus the indicator function for the relative complement of Y in X2 (id est: X2 \\ Y); it should be noted that all functions mentioned are defined on all of O but have nonzero values according to only the previous description (in particular, u = 0 identically in O \\ X2); the indicator functions directly are functions of the input X1. See also: "zdeltakronekre", "zdeltadirake".