Bogachev V.I. Measure Theory. Volume 1

Springer, 2007. — 514 p.This book gives an exposition of the foundations of modern measure theory and offers three levels of presentation: a standard university graduate
course, an advanced study containing some complements to the basic course (the material of this level corresponds to a variety of special courses), and, finally, more specialized topics partly covered by more than 850 exercises. The target readership includes graduate students interested in deeper knowledge of measure theory, instructors of courses in measure and integration theory, and researchers in all fields of mathematics. The book may serve as a source for many advanced courses or as a reference.