Hello every one, let be V an open convex a a normed vectorial space E.(adsbygoogle = window.adsbygoogle || []).push({});

Let be ##(a_{n}) \in \mathbb{R}^{n}## with ##\sum_{i \in \mathbb{N}} a_{i} = 1##.

Let be ##(v_{n}) \in V^{\mathbb{N}}## as ##\sum_{i \in \mathbb{N}} a_{i}v_{i}## exists.

Does necessarly ##\sum_{i \in \mathbb{N}} a_{i}v_{i} \in V## please?

Thank you in advance and have a nice afternoon.

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# Convexe and serie

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