Minkowski Inequality

an inequality of the form

where a_k and a_k (k = 1,2, . . . , n) are non-negative numbers and r > 1. The Minkowski inequality has analogs for infinite series and integrals. The inequality was established by H. Minkowski in 1896 and expresses the fact that in n-dimensional space, where the distance between the points x = (x₁, x₂, . . . , x_n) and y = (y₁, y₂, . . . , y_n) is given by

the sum of the lengths of two sides of a triangle is greater than the length of the third side.