Minimum sum equals sum of minima?

Hello everyone!

If we have functions, f1(t), f2(t), etc. all positive in our observation window, plus:
for all , does it follow that:
?

i.e. is the saying "minimum sum equals sum of minima" correct here?


Thanks!

It does follow from a basic theorem in analysis. That is, the theorem holds when N = 2, and I think you could induct on N.