Summation of the Max Distance between the elements of two sets

Question

I have a situation where I need to sum of the max distance of all elements of a Set $A$ comparing with all the elements of a set $B$.

For example: let's say that $dist(a,b)$ is the euclidean distance. Then I would have the following formula: $\sum_{a \in A} max(dist(a,B))$

But I'm not sure if this notation $max(dist(a,B))$ would be clear enough to denote the return of the distance of $a$ to the most far element in $B$ because it would be inconsistent with the distance function $dist(a,b)$ since the second parameter is an element of $B$ and not the set itself.

Do you know any notation that would make this summation of the maximum distances more clear and accurate?

Thanks!

Answer 1

In fact, if $a$ is a point and $B$ is a set, the notation $d(a,B)$ usually means the minimum distance from $a$ to the elements of $B$.

For the sum, you can write $$\sum_{a\in A}\max\{d(a,b):b\in B\}$$