For an integrable function f on [0, 1)ᵈ, let S (f) and Mf denote the corresponding dyadic square function and the dyadic maximal function of f, respectively. The paper contains the proofs of the ...

The Annals of Probability, Vol. 7, No. 6 (Dec., 1979), pp. 1051-1055 (5 pages) An inequality for certain random sequences more general than martingales or nonnegative submartingales is proved. Three ...