A simple proof of the triangle inequality for the NTV metric Original Research Article

We study a certain metric d on View the MathML sourcen that was recently introduced by Nieto, Torres and Vázquez-Trasande [1], give a simple proof for the triangle inequality, and describe when exactly d(p, q) = d(p, r) + d(r, q) holds for some p, q, r ϵ View the MathML sourcen. Remarkably, one has d(p, q) = 2 for some p, q ϵ View the MathML sourcen if and only if 0 = p + q ≠ p holds, in which case, one has also d(p, q) = d(p, r) + d(r, q) for all r ϵ View the MathML source.