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No return to convexity

Jakub Onufry Wojtaszczyk (2010)

Studia Mathematica

We study the closures of classes of log-concave measures under taking weak limits, linear transformations and tensor products. We investigate which uniform measures on convex bodies can be obtained starting from some class 𝒦. In particular we prove that if one starts from one-dimensional log-concave measures, one obtains no non-trivial uniform mesures on convex bodies.

Norms for copulas.

Darsow, William F., Olsen, Elwood T. (1995)

International Journal of Mathematics and Mathematical Sciences

On an Invariant Borel Measure in Hilbert Space

G. Pantsulaia (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

An example of a nonzero σ-finite Borel measure μ with everywhere dense linear manifold μ of admissible (in the sense of invariance) translation vectors is constructed in the Hilbert space ℓ₂ such that μ and any shift μ ( a ) of μ by a vector a μ are neither equivalent nor orthogonal. This extends a result established in [7].

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