Also Kai Lai Chung's "A Course in Probability Theory" is excellent. One drawback is that it has a few typos but that keeps you sharp ;-). 4 Measure Theory We largely follow Bauer’s textbook [1] for our formalization of measure theory. If the inline PDF is not rendering correctly, you can download the PDF file here. If you want to go deeper into probability theory: I would also recommend Heinz Bauer's "Measure and integration theory". xvi+472. In integration theory, specifying a measure allows one to define integrals on spaces more general than subsets of Euclidean space; moreover, the integral with respect to the Lebesgue measure on Euclidean spaces is more general and has a richer theory than its predecessor, the Riemann integral. 4.1 The ˙-algebra We use records to represent (˙-)algebras and measure spaces. 538 pages.
236. Bourbaki, Nicolas (2004).

References Agresti,A. ISBN 978-3-11-016719-1. Measure and Integration Theory. Responsibility: Heinz Bauer. file download fiwu.pdf Heinz Bauer.

Chapters 1–6. Probability theory and elements of measure theory. Integration. … I. Mathematics. [5] Józef Białas. Measure Theory Integration Theory Product Measures Measures on Topological Spaces Bibliography Index: Series Title: De Gruyter studies in mathematics, 26. Berlin: Springer-Verlag. But I found it a bit dry (in German). 0120828200, 9780120828203. Heinz Bauer.
Other Titles: Mass- und Integrationstheorie .

An exception is the de nition of the Lebesgue integral which is taken from Schilling [12]. (2015).Foundations of linear and generalized linear models.Hoboken,NJ:JohnWiley& Sons. Translated from the 1959, 1965 and 1967 French originals by Sterling K. Berberian. Probability Theory. Measure and Integration Theory.

The σ-additive measure theory. This is one of the best introductions to this subject I have ever seen (and my professor and some others seem to agree). However, I'd also suggest Measure and Integration Theory by Heinz Bauer.

MR 2018901. Walter de Gruyter Inc., 2002. Elements of Mathematics (Berlin). These notes have been created for the \Measure and integration theory" part of a course on real analysis at the TU Delft.

De Gruyter Studies in Mathematics 26. from the German by Robert B. Burckel. 460 pages. Measure theory. ... Heinz Bauer. Berlin: De Gruyter. Bauer, Heinz (2001).

Dudley, … Series of positive real numbers. It is a translation of the author's original book in German where only the relevant topics are kept. We de ne measure spaces as extensions to algebras, hence we can use measure spaces as algebras. ISBN:9783110814668 of pdf Jan 1, 1997. Transl. [6] Józef Białas. Measure and integration theory; Probability theory; Continuation of measure and integration theory; Further development of probability theory. Bauer,H. 414 pages. ISBN 3-540-41129-1. Formalized Mathematics, 2(2):263-270, 1991. Together with the rst part of the course on metric spaces, these notes form the mathematical basis for several bachelor courses and master courses in applied mathematics at TU Delft. Formalized Mathematics, 2(1):173-183, 1991. Jan 1, 1996.