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The Cramér-Wold theorem
 Pešek, Matěj ; Nagy, Stanislav (advisor) ; Beneš, Viktor (referee)
The Cramér-Wold theorem asserts, that every d-dimensional (Borel) probability me- asure can be characterized by the P-probabilities of all halfspaces (sets of points lying on one side of a given hyperplane). Equivalently, the distribution of each d-dimensional random vector X is fully described by all distributions of projections ⟨X, u⟩, for u from the unit sphere. The goal of this thesis is a detailed proof of this important theorem, and a discussion on its potential extensions. Do we really need to know all projections ⟨X, u⟩ for each u? Projections in how many directions are necessary to be known to be able to determine a measure P, which assigns to n distinct points masses 1/n? How does the Cramér-Wold theorem relate to similar results used outside of the probability theory? 1
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