Geometry of good sets in n-fold Cartesian product

We propose here a multidimensional generalisation of the notion of link introduced in our previous papers and we discuss some consequences for simplicial measures and sums of function algebras.Comment: 17 pages, no figures, no table

Supports of Gaussian measures

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Shift invariant measure and simple spectrum

We consider some descriptive properties of supports of shift invariant measures on CZ under the assumption that the closed linear span (in L2) of the co-ordinate functions on CZ is all of L2

Measure free martingales and martingale measures

Let T ⊂ R be a countable set, not necessarily discrete. Let ft, t ∈ T, be a family of real-valued functions defined on a set Ω. We discuss conditions which imply that there is a probability measure on Ω under which the family ft, t ∈ T, is a martingale

Mathematics of risk taking

A simple mathematical model for an investor's gains and losses over time shows that, in the long run, those with large sums to invest have an excellent chance of reaching their goal while the marginal investors have a high probability of going bankrupt. A greedy investor, rich or poor, will hit the bottom in the long run, with probability one. Consequences for the population at large are discussed