Books, like travellers, ought to say at the door why they have come. This one has come to teach the theory of measure: the discipline that tells us, with a rigour the calculus never quite managed, what it means for a set to have a size, for a function to have an integral, and for a sequence of either to converge. It is written for the student who has met the Riemann integral and suspects, correctly, that it has not told the whole truth; for the graduate who must use the Lebesgue integral daily and would like, for once, to see it built rather than invoked; and for the working scientist-the statistician, the physicist, the engineer, the physician reading a paper on survival analysis-who meets the phrase "almost everywhere" and wishes to know what it is excusing. Its purpose is not to add one more formulary to a crowded shelf. It is to show, step by step and with every step justified, how a handful of definitions about sets becomes the language in which modern analysis, probability and much of mathematical physics are written; and to show it in such a way that the reader could, with patience and a blank sheet, have built it too. The book is published by the Scottish Science Society, a British non-profit institution whose single purpose is to disseminate consistent knowledge from every field of science, and to do so without prejudice and without religion. The two refusals are meant in the most practical sense. We do not ask where a reader comes from, what they believe, or what they have been told they are capable of; and we do not ask a theorem to flatter anyone, since a theorem that flattered would no longer be one. What we ask of our books is that they be consistent-that each statement follow from what has gone before-and what we ask of our readers is only that they be willing to check. The two requests turn out, on inspection, to be the same request made from opposite ends of the page. A word on the editions, which the reader deserves to hear before paying for one. We publish first a softcover in black and white, and we do so for accessibility: it is the edition that the largest number of students can afford, and every figure in the book has been drawn so that it can be read in shades of grey, with hatching and tone doing the work that colour does elsewhere. If the treatise contains fewer than five hundred pages, we publish as well a hardcover in colour for those who prefer it. Nothing is lost in the softcover and nothing is added to the hardcover but a little comfort in the hand, a little pleasure to the eye-and, as is unavoidable with colour printing, a little more in the price. We apologise for theinconvenience. It is the only inconvenience in the book that is not a theorem. Finally, and not least: please write to the author, at richard@scottishsciencesociety.org, with your impressions, your criticisms, the errors you have found and the proofs you think could be shorter. He is a lovely fellow who loves to chat, and has made many, many friends through exactly that vein of correspondence-which is the more remarkable in a man usually reserved to his home and devoted, in roughly descending order of their claims upon his attention, to his greyhounds, his books, a great deal of reading and, well, medicine. The greyhounds, it should be said, have read none of this treatise, and have been of no help with the proofs; but they have sat through all of them with a patience that the author recommends to every reader who reaches Chapter 4.
