Here we study the almost sure almost everywhere convergence of random series of the form ∑∞ i=1 aifi in the Lebesgue spaces L p(X,Σ, μ), where the ai’s are centered random variables, and the fi’s constitute an unconditional basic sequence or an lp stable sequence. We show that if one of these series converges in the norm topology almost surely, then it converges almost everywhere almost surely.

Secure multi-party computation (MPC) is a central problem in cryptography. Unfortunately, it is well known that MPC is possible if and only if the underlying communication network has very large connectivity — in fact, , where is the number of potential corruptions in the network. This impossibility result renders existing MPC results far less applicable in practice, since many deployed network...

A Turing degree a is said to be almost everywhere dominating if, for almost all X ∈ 2 with respect to the “fair coin” probability measure on 2, and for all g : ω → ω Turing reducible to X, there exists f : ω → ω of Turing degree a which dominates g. We study the problem of characterizing the almost everywhere dominating Turing degrees and other, similarly defined classes of Turing degrees. We r...

1. In this paper we will give necessary and sufficient conditions for a measurable function to be equivalent to one which is differentiable a. e. on a set E. The condition is in terms of Marcinkiewicz type integrals which have also been recently the main objects in problems of differentiability. The reader is especially referred to the important paper on differentiability by E. M. Stein and A. ...

Maximal estimates for Schrödinger means and convergence almost everywhere of sequences are studied.