Almost everywhere generalized phase retrieval

Incentive Compatibility: Everywhere vs. Almost Everywhere∗

A risk neutral buyer observes a private signal s ∈ [a, b], which informs her that the mean and variance of a normally distributed risky asset are s and σ s respectively. She then sets a price at which to acquire the asset owned by risk averse “outsiders”. Assume σ s ∈ { 0, σ } for some σ > 0 and let B = { s ∈ [a, b] | σ s = 0 } . If B = ∅, then there exists a fully revealing equilibrium in whic...

Almost Everywhere Convergence of Poisson Integrals on Generalized Half-planes

Almost-Everywhere Secure Computation

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...

Almost everywhere domination

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...

Differentiability Almost Everywhere

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. ...