Real Variables (repost)

Inadequate index, but good text, January 11, 2009

This review is from: Real Variables (Paperback)
I previously wrote the following paragraphs regarding the inadequacy of the index. One commentator has rebuked me (justly) for reviewing an essentially unread book. Well, I've consulted the book often since the original review, and apart from the still-inadequate index, admit that I like it. I'm not prepared to review it in detail, but I wanted to modify my previous ranking to more accurately reflect my updated outlook on the text's usefulness for teaching real variables. Here is the original review, in which I had given the book one star:

I have only perused the book in anticipation of an upcoming class, and used it as a supplemental text to Royden's Real Analysis. The one-star rating I have given at this point applies only to the index, which is abysmal. The index groups each term under the category to which it belongs. For example, when I look for "Radon-Nikodym Theorem," it is not located in the "R" section. It is instead in "S" under "Signed Measure" as the main heading with "Radon-Nikodym Theorem" as a subheading! Now, such a topic-oriented index may well be useful, but it should be in addition to the standard index, not in place of it! As another example, if one wants to see what Torchinsky has to say about "spectral decomposition," one must look not in the "S" section but rather the "C" section under "Compact mapping" where "spectral decomposition" exists as a subheading! This flaw is particularly annoying when using the book as a reference text in support of another text. The index is virtually worthless in this case, unless one is willing to scan the index for each topic of interest. Which, by the way, is not that difficult since the index is only 4.5 pages long.

Again, my low rating applies only to the index; so far what I've seen in the text itself appears commendable. I hope to write a full review at the end of this semester. I can say that no matter how outstanding the text may be, I will never be able to rate above 4 stars due to the inadequacy of the index.