given this summation $\sum_{t=1}^T \sum_{s= \lfloor g(t) \rfloor}^t x_{t,s}$, where $g(t)$ is an increasing function satisfying $g(t)\leq t$ for all $t$, is it possible to swap the indexes of the two sums?
I have been thinking it should be equivalent to $\sum_{s=\lfloor g(1) \rfloor}^T \sum_{t= \lfloor g^{-1}(s) \rfloor}^T x_{s,t}$, is it correct?