Uniform Central Limit Theorem for martingales

We study some sufficient conditions imposed on the sequence of martingale differences (m.d.) in the separable Banach spaces of continuous functions defined on the metric compact set for the Central Limit Theorem in this space. We taking into account the classical entropy terms, and use the theory of the so-called Grand Lebesgue Spaces of random variables having power and exponential decreasing tail of distribution

Reassessing the Citizens Protection Act: A Good Thing It Passed, and a Good Thing It Failed

The Citizens Protection Act (CPA) of 1998 has always been a lightening rod for criticism, and it remains so today. This article reassesses the CPA’s perceived inadequacies in light of how it has actually affected (or, not affected) federal prosecutors’ involvement in criminal investigations. The article takes issue with the critics and demonstrates that the CPA succeeded where it should have, failed where it should have, and left us—however inadvertently—with a remarkably coherent and consistent approach to regulating federal prosecutors’ involvement in criminal investigations regardless of whether a suspect retains counsel early in the proceedings. The CPA requires federal prosecutors to follow state rules of professional conduct “to the same extent and in the same manner” as all other lawyers. The CPA was intended to—and did—nullify a U.S. Department of Justice (DOJ) declaration that unilaterally exempted federal prosecutors from much of the “no-contact” rule, which prohibits a lawyer in a matter from communicating with the client of another lawyer in the matter. The CPA was also intended to—but did not—require federal prosecutors to comply with various state interpretations of the no-contact rule that might have restricted their ability to participate in both covert and overt communications with represented criminal suspects. It is a good thing the CPA passed because DOJ’s assertion of authority over the no-contact rule for its own lawyers would inevitably have undermined public confidence in federal prosecutors’ commitment to fair and ethical investigatory processes. By the same token, it is a good thing that the CPA failed because broadly depriving DOJ of federal prosecutors’ involvement in communications with represented suspects would have substantially hindered criminal investigations for no good reason