"|" usually means "condition on", is this what it does mean here?

Question

Page 68 in pattern recognition and machine learning (free) uses this form

$p(x = 1|μ) = μ$

to denote the probability of a single binary random variable x = 1.

"|" usually means "condition on", is this what it does mean here?

Answer 1

Yes, that means that the probability of the event $x=1$ given that the parameter $\mu$ is equal to $\mu$ (another words, given the value of $\mu$) is equal to $\mu$.