Higher order monotonic (multi-) sequences and their extreme points

Functions on the half-line which are non-negative and decreasing of a higher order have a long tradition. When normalized they form a simplex whose extreme points are well-known. For functions on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{N}_{0} = \{0, 1, 2, . . .\}}$$\end{document} the situation is different. Since an n-monotone sequence is in general not the restriction of an n-monotone function on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}_{+}}$$\end{document} (apart from n = 1 and n = 2), it is not even clear at the beginning if the normalized n-monotone sequences form a simplex. We will show in this paper that this is actually true, and we determine their extreme points. A corresponding result will also be proved for multi-sequences. The main ingredient in the proof will be a relatively new characterization of so-called survival functions of probability measures on (subsets of) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}^n}$$\end{document}, in this case on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{N}^{n}_{0}}$$\end{document}.