A general convergence theorem

A General Theorem on the Convergence of Operator Semigroups

In all of these theorems the notion of convergence used in (1-1) and (1-2) has essentially been strong convergence. It is the purpose of the present paper to prove analogous theorems for a certain class of notions of convergence, which will include, in the case of Banach spaces of functions with the sup norm, bounded, pointwise convergence, and convergence of bounded sequences which is uniform ...

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 metastable dominated convergence theorem

The dominated convergence theorem implies that if (fn) is a sequence of functions on a probability space taking values in the interval [0, 1], and (fn) converges pointwise a.e., then ( ∫ fn) converges to the integral of the pointwise limit. Tao [26] has proved a quantitative version of this theorem: given a uniform bound on the rates of metastable convergence in the hypothesis, there is a bound...

A Convergence Theorem For Controlled . . .

A General Correlation Theorem