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Using the results presented in the previous lecture, namely the generalization of the Tsirelson's theorem [2] to mixed volumes, we calculate the mixed volume of the closed convex hulls of the two orthogonal Wiener spirals. Recall that the Wiener spiral is a set of functions of the form {1[0,t](·) : t ∈ [0, 1]} ? L2[0, 1]. This concept introduced by Kolmogorov is an important object in functional analysis.
[1] V. N. Sudakov. Geometric problems in the theory of infinite-dimensional probability distributions.
// Proc. Steklov Inst. Math., 141:1-178, 1979. Cover to cover translation of Tr. Mat. Inst.
Steklov 141 (1976).
[2] B. S. Tsirelson. Geometrical approach to the maximum likelihood estimation for infinitedimensional
Gaussian location. II. // Teor. Veroyatnost. i Primenen., 30(4):772-779, 1985.
[3] H. Minkowski. Theorie der konvexenK¨orper, insbesondere Begr¨undung ihres Oberfl¨achenbegriffs
// Gesammelte Abhandlungen, 2:131-229, 1911.
[4] R. Schneider. Convex bodies: the Brunn-Minkowski theory.- Cambridge: CambridgeUniversity
Press. - 2014. | 
