Additional Properties of Step Functions
Vigirdas Mackevičius · 2014
This chapter considers the integrals of functions of several variables (including functions of a single variable). The notion of a step function in the multidimensional case is extended. Instead of the uniform convergence of sequences of step functions, the convergence in another, much weaker sense will be required. Therefore, the class of limit functions will be significantly wider, and a more general Lebesgue integral will be obtained. This integral will possess very good properties. The chapter provides a series of problems to be solved.