Measure Theory

My main purpose in this book is to present a unified treatment of that part of measure theory which in recent years has shown itself to be most useful for its applications in modern analysis. If I have accomplished my purpose, then the book should be found usable both as a text for students and as a sour ce of refer ence for the more advanced mathematician. I have tried to keep to a minimum the amount of new and unusual terminology and notation. In the few pI aces where my nomenclature differs from that in the existing literature of meas ure theory, I was motivated by an attempt to harmonize with the usage of other parts of mathematics. There are, for instance, sound algebraic reasons for using the terms "lattice" and "ring" for certain classes of sets-reasons which are more cogent than the similarities that caused Hausdorff to use "ring" and "field. " The only necessary prerequisite for an intelligent reading of the first seven chapters of this book is what is known in the Uni ted States as undergraduate algebra and analysis. For the convenience of the reader, § 0 is devoted to a detailed listing of exactly what knowledge is assumed in the various chapters.