What does this $[\mu]$ mean here? 
Here's what those notation means

This $"[\mu]"$ makes the setence weird and I don't understand what it means
Please help
Here's the link of the whole paper, and this is at page 151 https://projecteuclid.org/download/pdf_1/euclid.acta/1485892007
 A: Almost all means the set of $x\in X$ you are looking at is all elements but a set with measurement $0$.
However, the notion of measurement $0$ depends on the measure $\mu$ you are using. So the $[\mu]$ in the theorem is supposed to remind you of that fact.
Note that the measurement $0$ can be way more than just the $0$ element!
For example with the standard Lebesgue measure $\mu$ the set $\mathbb{Q}$ is a $0$-measure subset of $\mathbb{R}$!
A: This "$[\mu]$" is used as a part of the following equivalent constructions:
-"almost all $[\mu]$"
-"almost everywhere $[\mu]$"
-"almost surely $[\mu]$"
Their meaning is the following:
If we say, that almost all $[\mu]$ elements of a measurable space $(X, \Omega, \mu)$ have some property, that means that the measure $\mu$ of the set of all elements of it that do not have this property is equal to zero. 
We write $[\mu]$ here, to explicitly say what measure were we talking about, as having several distinct non-equivalent measures can otherwise lead to confusion:
For example, almost all real numbers are non-zero under Lebesgue measure, but almost all of them are zero under the corresponding Dirac measure.
