I'm looking for a definition for a particular function(-input) property. Considering a function $f$ that takes as input a list of elements and produces in output just one element, which is the property that says that the result of $f$ for a given list of elements is EQUAL to the result of the same function $f$ that takes as input a list of elements which are the results of $f$ on subset to the given list?
I provide here some example because I understand the description is quite messy: Given the list [1,2,3,4,5] the first two examples abide by the property meanwhile the third does not:
$max([1,2,3,4,5]) = 5 = max([max([1,2]),max([3,4,5])])$ $avg([1,2,3,4,5]) = 3 = avg([avg([1,2]),avg(),avg([4,5])])$ $avg([1,2,3,4,5]) = 3 \neq 2,75 = avg([avg([1,2]),avg([3,4,5])])$
Personally, I think is a sort of functions associativity and I think the second case is just a fortuitous one.