Uvod u teoriju mjere i integracije

The textbook Introduction to the Theory of Measure and Integration by Dragan Jukić, published in 2008 by the Department of Mathematics at the University of Osijek (Element), is a fundamental work intended for students of mathematics, physics and related technical sciences. The book was created as a result of many years of teaching work and covers the key areas of modern mathematical analysis, without which it is impossible to understand modern probability theory, functional analysis and differential equations. The content of the textbook explains in detail the construction of the abstract theory of measure, starting with set algebras and $\sigma$-algebras, external measures and Carathéodory's theorem on the extension of measure. The central part of the book is devoted to the introduction of the Lebesgue integral, its properties, and key theorems on the replacement of the order of the integral and the limit value (monotone convergence theorem, Fatou's lemma, dominated convergence theorem). Spaces of integrable functions $L^p$, product measures and Fubini's theorem are specially treated. Due to the clear methodology, precise proofs and numerous solved examples, this edition is indispensable literature for higher education teaching.