A brief introduction to Banach spaces, their duals and L^p 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.

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Simon Eveson 17/10/2001