Is there in measure theory/topology the concept of "almost inclusion"?
Possible definition:
In a measurable space $(X,\mu)$ one set $A$ is almost included in another set $B$ if $A$ is included in $B$ to less than a finite number of zero-measure points.
Example:
$$A=\{-1\}\cup[2,3]\text{ and }B=[1,4]\;\Rightarrow\;A\;\dot\subset \;B$$
Where $\dot\subset$ is the symbol of almost inclusion (I don't know if that is used, but there is the inclusion symbol and a dot that reminds me of the fact that it is less than a finite number of zero-measure sets, so I used it)
If this definition already exists, what are the analogous symbols to indicate: $A\subset B$ and $a\in A$ (the second symbol should be a sort of "almost in")
I state that I searched online if it existed, but I didn't find anything, even if they seem to me quite usable definitions.