Locally Estimated Operators
These are versions of operators which take a function and an element in the domain of the function to give a locally weight estimation of those operators. Specifically, we'll be focusing on averages and variances.
Local average operators are a class of operators. An operator A: (I: T -> Y) * T -> Y, where T and Y are subsets of the set of real numbers R, is a local average operator if the following hold for some b, such that b is less than or equal to all t in T, and some L: T * T -> Y :