Definition talk:General Euclidean Metric

The literature that I have to hand specify the General Euclidean Metric for integer $r$ only. Intuitively it seems sound to extend to $\R$ and from what I can tell Minkowski's Inequality holds for real $r \ge 1$ ... am I okay to assume that my source work is careless? (I would not be surprised - it's not the cleanest exposition I've seen.) --prime mover (talk) 22:03, 29 October 2012 (UTC)


 * Yes. Cf. Definition:P-Seminorm for a general treatment (in fact, coming to think of it, the general Euclidean metric is an instance of the metrics these norms induce - how general is measure theory). --Lord_Farin (talk) 22:40, 29 October 2012 (UTC)


 * "For applications in analysis," says Sutherland, p.32 op.cit., "metric spaces have a strong rival in normed vector spaces. The latter are particularly convenient for generalizing differential calculus and for handling linear problems in general ..."--prime mover (talk) 22:57, 29 October 2012 (UTC)