EDB — 116

[116]Let in the following \(X\) be a normed vector space based on the real field \({\mathbb {R}}\), with norm \(\| \cdot \| \). Let \( (f_ n)_{n\in {\mathbb {N}}}\) be a sequence of elements of \(X\). The series \(∑^∞_{n=0}f_ n\) converges totally when \(∑^∞_{n=0}\| f_ n\| {\lt}∞\).