Measure Integral

In this book, we introduce for the first time the notions of neutrosophic measure and neutrosophic integral, and we develop the 1995 notion of neutrosophic probability. We present many practical examples. It is possible to define the neutrosophic measure and consequently the neutrosophic integral and neutrosophic probability in many ways, because there are various types of indeterminacies, depending on the problem we need to solve. Neutrosophics study the indeterminacy. Indeterminacy is different from randomness. It can be caused by physical space materials and type of construction, by items involved in the space, etc. Keywords: Neutrosophics, Neutrosophic Measure, Neutrosophic Integral, Neutrosophic Probability, Neutrosophic Logic, Neutrosophic Set, Neutrosophy

This volume develops the classical theory of the Lebesgue integral and some of its applications. The integral is initially presented in the context of n-dimensional Euclidean space, following a thorough study of the concepts of outer measure and measure.

The Lebesgue Integral, Simple Functions, Non-Negative Functions

This book is devoted to integration, one of the two main operations in calculus.
In Part 1, the definition of the integral of a one-variable function is different (not essentially, but rather methodically) from traditional definitions of Riemann or Lebesgue integrals. Such an approach allows us, on the one hand, to quickly develop the practical skills of integration as well as, on the other hand, in Part 2, to pass naturally to the more general Lebesgue integral. Based on the latter, in Part 2, the author develops a theory of integration for functions of several variables. In Part 3, within the same methodological scheme, the author presents the elements of theory of integration in an abstract space equipped with a measure; we cannot do without this in functional analysis, probability theory, etc. The majority of chapters are complemented with problems, mostly of the theoretical type.