## Notes on l^p space [1≤p≤∞]: Definition, Examples, Metric

For 1≤p<∞, let us consider the following set of sequences in the linear space K, denoted by lp: lp = {(x1, x2, … ): xi ∈ K, $\sum_{i=1}^\infty$ |xi|p<∞}. For x = (x1, x2, …) and y = (y1, y2, …) ∈ lp, define dp(x, y) = ($\sum_{i=1}^\infty$ |xi – yi|p)1/p. Next, we prove that … Read more