Assume that there are several geographical regions and within each region there may be many buildings. Buildings may or may not be created and destroyed from time to time hence the requirement to capture the total building area at a point in time (i.e., month).
I want to write the following in shorthand notation if possible.
Sum of the area of all buildings within a region that existed for a given month.
More generally I frequently need to describe various summations across sets of data (building areas, building energy consumption, etc) where the set is not a set of integers but a set of objects constrained by another set.
Is there a clear and succinct way to describe this mathematically and not through prose?