Articles written in Proceedings – Mathematical Sciences

• On the existence of a finite invariant measure

A necessary and sufficient condition is given for a Borel automorphism on a standard Borel space to admit an invariant probability measure.

• On the existence of automorphisms with simple Lebesgue spectrum

It is shown that ifT is a measure preserving automorphism on a probability space (Ω,B, m) which admits a random variable X0 with mean zero such that the stochastic sequence X0 o Tn,n ε ℤ is orthonormal and spans L02(Ω,B,m), then for any integerk ≠ 0, the random variablesX o Tnk,n ε ℤ generateB modulom.

• When isf(x,y) = u(x) + v(y)?

LetX andY be arbitrary non-empty sets and letS a non-empty subset ofX ×Y. We give necessary and sufficient conditions onS which ensure that every real valued function onS is the sum of a function onX and a function onY.

• Geometry of good sets inn-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.

• Measure free martingales

We give a necessary and sufficient condition on a sequence of functions on a set Ω under which there is a measure on Ω which renders the given sequence of functions a martingale. Further such a measure is unique if we impose a natural maximum entropy condition on the conditional probabilities.

• Measure Free Martingales and Martingale Measures

Let $T\subset\mathbb{R}$ be a countable set, not necessarily discrete. Let $f_t,t\in T$, 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 $f_t,t\in T$, is a martingale.

• Proceedings – Mathematical Sciences

Volume 130, 2020
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Continuous Article Publishing mode

• Editorial Note on Continuous Article Publication

Posted on July 25, 2019