[see also: event, possibility]
We first do the case $n=1$.
This argument also settles the case of $K= \Gamma$.
We finish by mentioning that, suitably modified, the results of Section 2 apply to the $AP$ case.
Note that (4) covers the other cases.
There are several cases to consider: ......
We close this article by addressing, in part, the case of what happens if we replace the map $T$ by convolution.
There are quite a number of cases, but they can be described reasonably systematically.
The general case follows by changing $x$ to $x-a$.
This abstract theory is not in any way more difficult than the special case of the real line.
Important cases are where $S=$ ......
This case arises when ......
Both cases can occur.
To deal with the zero characteristic case, let ......
Then either ......, or ...... In the latter $\langle$former$\rangle$ case, ......
In the case of finite additivity, we have ......
In the case of $n\ge 1$ $\langle$In case $n\ge 1\rangle$, ...... [ Better: If $n\geq 1$ then ......]
In the case where $A$ is commutative, as it will be in most of this paper, we have ......
We shall assume that this is the case.
It cannot be that there exists $x \in \Omega \setminus F$, for otherwise $\theta(\delta_x) = \kappa_E(\delta_x) =0$, which is not the case.
Unfortunately, this is rarely the case.
However, it need not be the case that $V> W$, as we shall see in the following example.
Such was the case in (8).
The $L^2$ theory has more symmetry than is the case in $L^1$.
Note that some of the $a_n$ may be repeated, in which case $B$ has multiple zeros at those points.
This is handled by a direct case-by-case argument.
a classic $\langle$textbook/typical/borderline/simple/extreme/rare/striking$\rangle$ case
We use upper case letters to represent inverses of generators. [= capital letters]
Go to the list of words starting with: a
b
c
d
e
f
g
h
i
j
k
l
m
n
o
p
q
r
s
t
u
v
w
y
z