Let there be a sum $\sum_{k \geq 1}^{}\sum_{j \geq 1}^{} d(F_{j,k})^p$ where $F_{j,k}$ are sets of $\mathbb{R}^n$ and $d$ is defined as the diameter of the sets.
Why can we say that we might change the order of that sum randomly and get the same value? Remark please that I know that I might change the order of every sum whose limit is finite as long as the sum of absolute values of the summands converges. My question is more about the case whether we get for every sum with changed order $\infty$ if $\sum_{k \geq 1}^{}\sum_{j \geq 1}^{} d(F_{j,k})^p=\infty$.