A strong law of large numbers on the harmonic \(p\)-combination (Q639978)

The classical Brunn-Minkowski theory has a natural extension in what became known as the \(L_p\) Brunn-Minkowski theory. The harmonic \(p\)-combination which is the generalization of the Firey-Minkowski \(L_p\) combination of convex bodies was introduced in [\textit{E. Lutwak}, Adv. Math. 118, No.~2, 244--294 (1996; Zbl 0853.52005)]. In this paper, the authors establish a strong law of large numbers for the harmonic \(p\)-combination of random star bodies. The organization of the paper is as follows. In Section 2, the authors set notations and give preliminaries. Section 3 is denoted to the establishment of the strong law of large numbers on the harmonic \(p\)-combination.