There are many ways to explain $\ell _p$ space, but how to make it into a single math notation?
It is my guess that a space of infinite sequences of real numbers can be defined as
$ \ell ^p ( \mathbb{R}) := \left\{ \mathbf{v} = (v_n)_{n \in \mathbb{N}} \ \Bigg| \ \left\| \mathbf{v} \right\| _p < \infty \right\} \ \ \text{for any} \ p \in \mathbb{R}^+ $.
Is it correct? Any ideas? Thanks.
To avoid circularity and be a bit more explicit, I'd go with:
$$\ell_p(\Bbb R):=\left\{v=(v_n)_{n\in\Bbb N}\in\Bbb R^{\Bbb N}\,\middle\vert\, \sum_{n=0}^\infty \left\lvert v_n\right\rvert^p<\infty\right\}$$