## 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.