The Elements of an Analysis of the Functions of a Set

TL;DR

This paper introduces a new measure for set systems, a set variation concept, and derives conditions for optimizing functions of sets, advancing the mathematical analysis of set functions.

Contribution

It proposes a generalized measure for set systems, a set variation method, and necessary optimization conditions, enhancing the theoretical framework of set function analysis.

Findings

Introduces a new measure generalizing classical set measures.

Defines a set variation allowing derivative construction.

Provides necessary conditions for optimization of set functions.

Abstract

The variant of calculation of functions of set and their application is offered. In particular: the new measure of system of sets generalizing classical concept of a measure is entered; the variation of set that has allowed to construct a derivative of function of set on a measure is entered, and to receive necessary conditions of optimization in terms of function of set.