In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size. In this sense, a measure is a generalization of the concepts of length, area, and volume. Technically, a measure is a function that assigns a non-negative real number. Real analysis deals with the real numbers and real-valued functions of a real variable. Measure theory was developed in successive stages during the late 19th and early 20th centuries by Émile Borel, Henri Lebesgue, Johann Radon and Maurice Fréchet, among others. The main applications of measures are in the foundations of the Lebesgue integral, in Andrey Kolmogorov’s axiomatisation of probability theory and in ergodic theory. This book presents recent advances in measure theory and integration of measure theory and real analysis.

Print ISBN: 9781682500590 | $ 170 | 2016 | Hardcover

Contributors: Pape Djiby Mergane, Gane Samb Lo et al