Errata for Real Analysis with Real Applications
page Pgraph line change ----chapter 7------------------------------------------------------------------- 124 last 3 change "x,y in V" to "x,y,z in V" ----chapter l2------------------------------------------------------------------- 321 2 3 Before "Then ...", insert "Fix x_0>a. Let a_0 = sup {a} \cup { x : a < x <= x_0 tau(x) = 0 }. Notice that ||G(a_0)-F(a_0)|| \le delta. If a_0 = x_0, then G(x_0) = F(x_0) and the inequality is trivial. Otherwise, tau(x) > 0 on (a_0,x_0) and thus tau is differentiable on this interval." Change "Then" to "Then for x in (a_0,x_0), we have" 321 last 8 Change "a" to "a_0" in five places. 322 1 1 Change only the first two "a"'s to "a_0". 322 1 3 Change "a" to "a_0" in two places. 322 1 3 Add "In particular, the above inequality holds for x=x_0 and, as x_0 is an arbitrary point on (a,b], the result follows." -----------------------------------------------------------------------------
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