Une théorie de Denjoy des martingales dyadiques. (A Denjoy theory of dyadic martingales)
Following ideas of A. Denjoy, a theory of dyadic martingales is sketched, i.e. of sequences \((f_ n)^{\infty}_{n=0}\) of real-valued functions \(f_ n\) such that \(f_ 0\) is constant, \(f_ n(x)=f_ n(x_ 1,x_ 2,...,x_ n)\), were \(x=(x_ 1,x_ 2,...)\), \(x_ i=0\) or 1 for \(i=1,2,3,...\), and there holds \[ f_ n(x_ 1,x_ 2,...,x_ n)=2^{- 1}[f_{n+1}(x_ 1,...,x_ n,0)+f_{n+1}(x_ 1,...,x_ n,1)]. \]
scientific article; zbMATH DE number 4159780