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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Convexe and serie

**Physics Forums | Science Articles, Homework Help, Discussion**