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## Fourth Edition - Errata and Additions

- In D of Exercise 1.5.13, the exponent should be upper-case, so the
inequality should read
\(|x-x_n|\le \left(\frac{c+1}{c+2}\right)^N.\)
- All mention in running text of "Sunrise lemma" should be lowercase.
- All mention in running text of "Method of Exhaustion" should be lowercase.
- In solution to Exercise 6.5.7: \(W_\lambda\) should be \(U_\lambda\) throughout.
- In proof of Theorem 6.6.1: \(j\) should be \(j=\min\{k: m_k=m_*\}\).
- Citation for Conway in Chapter 1 footnote should be fixed.
- Sunrise figure in chapter 6 should be scaled 80% and fixed with psfrag.
- Add Holder/Lipschitz continuity as examples of uniform continuity in \(\S\)2.3.
- Add index entries for Holder/Lipschitz continuity in Chapters 2 and 6.
- Add problem 6.3.10: \(F\) Cantor implies \(1-F(x) = F(1-x)\).
- Add problem 6.5.8: \(F\) Cantor is differentiable exactly off \(C\), where \(F'\equiv 0\).
Use 6.3.10 and 6.5.7.
- Add index entries for Dini derivatives in Chapter 6.
- In $\S$1.1, the phrase "When $X$ and $Y$ are disjoint" is superfluous and should be deleted.
- The axiom of countable choice ($\S$1.1) is assumed because it is needed to establish the
subadditivity of area (equation (4.2.2) in $\S$4.2). This is the only use of this axiom in the text,
but of course the whole of the remainder of the text depends crucially on subadditivity.