FUNDAMENTAL THEOREMS IN A BAYES CONTROLLED PROCESS

A Fundamental Issue of Naive Bayes

Fundamental Theorems of Evolution.

Evolutionary biology is undergirded by an extensive and impressive set of mathematical models. Yet only one result, Fisher's theorem about selection and fitness, is generally accorded the status of a fundamental theorem. I argue that although its fundamental status is justified by its simplicity and scope, there are additional results that seem similarly fundamental. I suggest that the most fun...

The Fundamental Limit Theorems in Probability

1. Introduction. The main purpose of this address is to explain the mathematical content and meaning of the two most important limit theorems in the modern theory of probability: the central limit theorem 1 and the recently discovered precise form of what was generally known as "KolmogorofFs celebrated law of the iterated logarithm. v The former traces its origin to the very beginnings of the t...

Fundamental Domains , Lattice Density , and Minkowski Theorems

Now that we know that every lattice admits a basis, a next fundamental question is: given linearly independent vectors b1, . . . , bn ∈ L how can we tell if they form a basis of L? As we have seen previously, not every set of n linearly vectors in Zn is a basis of Zn. One possible answer is given in the following lemma. It says that the basic parallelepiped generated by the vectors should not c...

Topological regular variation: II. The fundamental theorems

This paper investigates fundamental theorems of regular variation (Uniform Convergence, Representation, and Characterization Theorems) some of which, in the classical setting of regular variation in R, rely in an essential way on the additive semi-group of natural numbers N (e.g. de Bruijn’s Representation Theorem for regularly varying functions). Other such results include Goldie’s direct proo...