I am trying to read a textbook on probability and am already stuck on what must be basic notation. It says
Thus, for example, if $A$ is any subset of $\mathbb{Z}^+$, it follows that for some $c$ not depending on $A$, $n$ or $p$, $$|\mathbb{P}[W \in A] - Po(np)\{A\}| \leq c \sum_{k\in A} \frac{(np)^k}{k!}e^{-np}\{np^2+k^2n^{-1}\}$$
Po is the Poisson distribution but what exactly does $Po(np)\{A\}$ mean? I am assuming the curly brackets on the right hand side of the inequality don't have any special meaning.
\begin{equation} |\mathbb{P}[W \in A] - Po(np)\{A\}| \end{equation} means the difference between the probability that the random variable $W$ takes a value in the set $A$ and the probability that a Poisson random variable with mean $np$ takes its value in the set $A$. So if we say $X \sim Po(np)$, we could re-write it as \begin{equation} |\mathbb{P}[W \in A] - \mathbb{P}[X \in A]|. \end{equation} For example, if $A = \{k\}$, where $k$ is just some positive integer, then it would be $|\mathbb{P}[W = k] - \mathbb{P}[X = k]|$, and $\mathbb{P}[X=k] = (np)^k e^{-np}/k!$. So your inequality is basically saying how 'close' the random variable $W$ is to a random variable that follows a Poisson distribution with mean $np$, in some sense.