what does this notation $Z1\{condition\}$ mean?

Question

I am reading that you can decompose a random variable like this:

$$ Z = Z1\{Z\leq\theta\mathbb{E}[Z]\} + Z1\{Z>\theta\mathbb{E}[Z]\} $$

What does $$Z1\{condition\} $$ mean in this case?

Thanks for your help.

Answer 1

$1_{\{condition\}}$ is an indicator function: $1$ when condition is true, $0$ when it is not. $Z 1_{\{condition\}}$ is just the random variable $Z$ multiplied by this.