论文信息 - An alternate formulation of mean value for random geometric figures *

An alternate formulation of mean value for random geometric figures *

In contrast to the traditional technique of averaging functionals of a random geometric figure, it is possible to consider an averaging process which treats the figure as a whole. The result in probabilistic terminology is an expectation, which is itself a figure. Theoretical foundations and various instances are presented in an informal survey.

R. A. Vitale

[1] Wassily Hoeffding,et al. On the Distribution of the Expected Values of the Order Statistics , 1953 .

[2] Y. Rozanov,et al. An Application of the Central Limit Theorem , 1961 .

[3] R. Aumann. INTEGRALS OF SET-VALUED FUNCTIONS , 1965 .

[4] E. Bolker. A class of convex bodies , 1969 .

[5] Z. Artstein,et al. A Strong Law of Large Numbers for Random Compact Sets , 1975 .

[6] Wolfgang Weil,et al. An application of the central limit theorem for banach-space-valued random variables to the theory of random sets , 1982 .

[7] W. Weil,et al. Zonoids and Related Topics , 1983 .

[8] J. Mecke. Extremal Properties of Some Geometric Processes , 1987 .

[9] Richard A. Vitale,et al. Expected Convex Hulls, Order Statistics, and Banach Space Probabilities * . , 1987 .

[10] J. Wieacker. Geometric Inequalities for Random Surfaces , 1989 .