A General Glivenko–Gödel Theorem for Nuclei

A More General Version of the Costa Theorem

In accordance with the Costa theorem, the interference which is independent of the channel input and known non-causally at the transmitter, does not affect the capacity of the Gaussian channel. In some applications, the known interference depends on the input and hence has some information. In this paper, we study the channel with input dependent interference and prove a capacity theorem that n...

A General Correlation Theorem

A general ballot theorem

We prove an analogue of the classical ballot theorem that holds for any random walk in the range of attraction of the normal distribution. Our result is best possible: we exhibit examples demonstrating that if any of our hypotheses are removed, our conclusions may no longer hold.

A Representation Theorem for General Revealed Preference

Following Richter (1966), we provide criteria under which a preference relation implied by a finite set of choice observations has a complete extension that can in turn be represented by a utility function. These criteria rely on a mapping over preference relations, the rational closure, which is a generalization of the transitive closure and is employed to construct the complete extension. We ...

A General Stone Representation Theorem

This note contains a Stone-style representation theorem for compact Haus-dorff spaces. The note is very much inspired by some existing representation theorems and is expository in nature. The first representation theorem is by Jung and Sünderhauf in [JS] and there is also a version of it for compact Hausdorff spaces noted by D. Moshier [Mo], the ideas of which were described to us by A. Jung. T...