I have a question pertaining to this. Before I did it as such I considered just partitioning by the naturals. Of course I realized that there were a plethora of problems with this but one in particular I wanted to ask about. I know that a partition of must have finite cardinality but does this still apply when either/or is ? I think the answer is yes, since technically does not make sense in the Riemann-Stieltjes sense (we of course obviate this by writing .