- #1
Calabi
- 140
- 2
Hello every one, let be V an open convex a a normed vectorial space E.
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.
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.