A brief introduction to Banach spaces, their duals and Lp spaces: errata and addenda.

Page numbers refer to the 10-point printed version distributed at the first lecture. The 12-point PostScript version on the WWW has been corrected.

Discussion between Exercise 1.2 and Definition 1.3, p.1
last expression should read $n\to\infty$, not $k\to\infty$.
Example 3.2, p.7
"$x\in S$" and "$x\notin S$" should read "$x\in A$" and "$x\notin A$".
Comments following Definition 3.3, first paragraph of p.8
Add at end "Moreover, if $f$ is measurable, $g$ is integrable and $|f|\leq g$ $\mu$-a.e.\ then $f$ is integrable."
Example 3.4, p.8
First sentence of Theorem 3.15, p.10
"$\mu$ is a complex measure on $\sigma$" should read "$\mu$ is a complex measure on $\Sigma$"
Sum should read "$$\sum_{j=1}^n c_j\chi_{A_j}$$".
Lemma 4.5, p.12
"a integrable function" should read "an integrable function".
Exercise 5.12, p.16
Last line should read "except in the degenerate case where $\Sigma$ does not contain two disjoint sets of non-zero measure".
line before equation (2), p.17
$\ell^p$ should read $L^p$

Thanks to Niall MacKay, Terence Jackson, Richard Clegg and Simon Kristensen.

Simon Eveson 17/10/2001