by D.H.Fremlin, University of Essex

In this treatise I aim to give a comprehensive description of modern abstract measure theory, with some indication of its principal applications. My intention is that the book should be usable both as a first introduction to the subject and as a reference work. The first two volumes are set at an introductory level; they are intended for students with a solid grounding in the concepts of real analysis, but possibly with rather limited detailed knowledge. The plan of the work is as follows:

  • Volume 1: The Irreducible Minimum
  • Volume 2: Broad Foundations
  • Volume 3: Measure Algebras
  • Volume 4: Topological Measure Spaces
  • Volume 5: Set-theoretic Measure Theory.
  • All five volumes have now been published (see sales). For more details, see contents and index (492KB); also the source files of Volume 1, Volume 2, Volume 3, Volume 4 and Volume 5, which are printed under copyleft. In the contents pages for individual chapters you will find the codes for TeX files of current drafts, and PostScript files of results-only versions.

    See here for errata so far observed in published volumes.

    Short reviews of Volumes 1 and 2 have been published in the August-September 2001 and August-September 2002 issues of American Mathematical Monthly.

    I have embarked on a kind of supplement, which will, if it is ever published, be in the form of a sixth volume Stochastic Calculus; a draft is available through mtcont.htm.

    Notes on difficulties with using TeX.

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