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\def\R{{\bf R}}
\centerline{\bf Errata of the second printing}
\bigskip
\noindent
{\bf Our thanks go to all our friends that have contributed to this list.}
\bigskip
On page 8, on the left side of the first formula from the
top, replace
$$
\biggl( \bigcup_i A^i_2 \biggr) (x_1) \ ,
$$
by
$$
\biggl( \bigcup_i A^i \biggr)_2 (x_1) \ .
$$
\bigskip
On page 11, last paragraph, replace
`$A_0 \subset \cal{A}$ and every $B \subset \Sigma$.'
by
`$A_0 \in \cal{A}$ with $\mu(A_0) < \infty$ and every $B \in
\Sigma$.'
\bigskip
On page 84, ninth line from the bottom, replace
$$
j_{\varepsilon}(x)=\varepsilon^{-n}j(\varepsilon/n)
$$
by
$$
j_{\varepsilon}(x)=\varepsilon^{-n}j(x/\varepsilon)
$$
\bigskip
On page 169, just before equation 11 it was stated that the
kernel of $e^{\{-t\sqrt{p^2+m^2}\}}$ can be computed explicitly
in three dimensions. In fact this can be done in any dimension
as was pointed out to us by Walter Schneider. The answer is
$$
e^{\{-t\sqrt{p^2+m^2}\}}(x,y)=2^{-{n-1 \over 2}} \pi^{-{n+1 \over 2}}
tm^{{n+1 \over 2}} (|x-y|^2+t^2)^{-{n+1 \over 4}}
K_{{n+1 \over 2}}(m(|x-y|^2+t^2)^{1/2}) \ ,
$$
for $x,y \in \R^n$. This follows from
$$
\int_{\S^{n-1}} e^{i \omega \cdot x} {\rm d} \omega
= (2 \pi)^{n/2} |x|^{1-{n \over 2}} J_{{n \over 2}-1}(|x|) \ ,
$$
and from
$$
\int_0^{\infty} x^{\nu +1} J_{\nu}(xy) e^{-\alpha(x^2+\beta^2)^{1/2}} {\rm d} x
$$
$$
=({2 \over \pi})^{1/2} \alpha \beta^{\nu+3/2} (y^2+ \alpha^2)^{-\nu/2 -3/4}
y^{\nu} K_{\nu+3/2}(\beta(y^2+\alpha^2)^{1/2}) \ .
$$
Here $J_{\nu}$ is the Bessel function of $\nu$-th order.
Using that
$$
K_{\mu}(z) \approx {1 \over 2} \Gamma (\mu) ({1 \over 2} z)^{-\mu}
$$
as $z \to 0$ and $Re \mu >0$,
we easily obtain formula (10) on page 169.
\bigskip
On page 235, fourth line from the bottom, in equation (3), replace
$4 \pi^2$ by $2 \pi^2$.
\bigskip
On page 146, fifth line before the end of Sect.~6.18, replace
`Such sets need not be `small', e.g. $\alpha$ could be all the rational
numbers, and hence $\alpha$ could be dense in $\Bbb{R}$. ' by
`Such sets need not be `small', e.g., $A$ could be all the rational
numbers, and hence $A$ could be dense in $\Bbb{R}$. '
\bigskip
\centerline{\bf Errata as of June 17, 1999}
\bigskip
On page 7, at the end of the fourth paragraph, replace `unit side length'
by `unit edge length'.
\bigskip
On page 11, seventh line after the statement of Theorem 1.4, replace
$B_2= A_1 \sim A_2$ by $B_2= A_2 \sim A_1$.
\bigskip
On page 11, second line from the bottom, replace `for every $A_0 \subset
{\cal A}$ and every $B \subset \Sigma$.' by `for every $A_0 \in {\cal A}$
with $\mu(A_0) < \infty$ and $B \in \Sigma$.'
\bigskip
On page 12, second and fourth line from the top, replace $A_i \subset
{\cal A}$ by $A_i \in{\cal A}$ and $B \subset \Sigma$ by $B \in \Sigma$.
\bigskip
On page 12, fourth line from the bottom, replace the sentence
`To prove measurability, note that when $f$ is lower
semi continuous then the set $\{x: f(x) < t + 1/j \}$ is measurable.' by the
sentence
`To prove measurability when $f$ is upper
semi continuous, note that the set $\{x: f(x) < t + 1/j \}$ is measurable.'
\bigskip
On page 16, in the middle integral of formula (8), replace $\mu({\rm d} x)$
by $\mu({\rm d} x) {\rm d}a$.
\bigskip
On page 16, on the third line of the penultimate paragraph replace
`Beppo--Levi' by `Levi'.
\bigskip
On page 17, delete the cautionary sentence in the statement of Theorem 1.6.
Since it has been assumed that the functions are summable, it is not necessary
to require that they be nonnegative. Delete the word {\it nonnegative} in
the hypothesis of the theorem. Add the following sentence at the beginning
of the proof:
\smallskip
We can assume that $f^1(x) \geq 0$ for otherwise just consider the functions
$f^j -f^1$ and $f-f^1$, which are nonnegative.
\bigskip
On page 23, in the statement of Theorem 1.10, replace
`Then $f$ is $\mu_2$-measurable, $g$ is $\mu_1$-measurable $\dots$'
by `Then
$f$ is $\Sigma_2$-measurable, $g$ is $\Sigma_1$-measurable $\dots$'
\bigskip
On page 23, in the fourth line from below, the formula
$$(A_1 \times B_1) \sim (A_2 \times B_2) =
[(A_1 \sim A_2) \times B_1] \cup [ A_2 \times (B_1 \sim
B_2)],$$ is incorrect and should be replaced by the formula
$$(A_1 \times B_1) \sim (A_2 \times B_2) =
[(A_1 \sim A_2) \times B_1] \cup [ (A_1 \cap A_2) \times (B_1 \sim
B_2)].$$
\bigskip
On page 32, second line in Exercise 6, replace `Remark (3)' by `Remark(4)'
\bigskip
On page 33, Exercise 15, third line after `{\it Hints}', replace
`construct a function $\psi \in C^0_c (\Omega)$' by
`construct a function $\psi_{\varepsilon} \in C^0_c (\Omega)$'
\bigskip
On page 36, eighth line from the bottom, replace
`{\bf essential supremum} of
$f$' by `{\bf essential supremum} of
$|f|$'
\bigskip
On page 40, sixth line from the bottom, after `assume that $\Omega = A$.'
add `(Why is $\int fg {\rm d}\mu$ defined?)'.
\bigskip
On page 41, in the penultimate line of the statement of Theorem 2.4, replace
$1 \leq p < \infty$ by $1