Suppose I have a variable with several indices, such as $C_{a,b,c,d}$, and I want to indicate the arithmetic mean. Such a mean is commonly denoted by $\mu$ or by an overbar. Is there any standard notation for the mean across only one particular dimension/index? For example, the average over the first index would be
$$ \overline{C_{b,c,d}} = \frac{1}{A} \sum_{a=0}^{A-1} C_{a,b,c,d} $$
but if I change the labels the notation with the overbar is ambiguous as to what quantity I'm averaging over.
Is there any standardised notation on the notation for the average across one particular dimension?