Definition:P-Sequence Metric
Jump to navigation
Jump to search
Definition
Real Sequences
Let $d_p: A \times A: \to \R$ be the real-valued function defined as:
- $\ds \forall x = \sequence {x_i}, y = \sequence {y_i} \in A: \map {d_p} {x, y} := \paren {\sum_{k \mathop \ge 0} \size {x_k - y_k}^p}^{\frac 1 p}$
The metric space $\struct {A, d_p}$ is the $p$-sequence space on $\R$ and is denoted $\ell^p$.