We establish relations between vertex operator algebras in mathematics and string path integrals in physics. In particular, we construct the basic representations of affine Lie algebras of [italic capitals]ÂD̂Ê-type using a method of string path integrals.
Is there a class of measures which is natural for sofic systems in the same way that Markov measures are natural for subshifts of finite type? Motivated by this question, we identify and study a class of finitary measures on sofic systems. We aim to convince the reader that, in …
After some measure-theoretic preliminaries, the notion of web is defined and used to construct a dimension- and metric-free setting for the differentiation of non-negative valued set functions. Conditions which guarantee the frequent existence of the derivative of one such funct…
The main results of this work can be formulated in such a way that they will attract a broad spectrum of mathematical interest, but the main audience includes combinatorialists, set-theorists, and topologists. This paper explores a central question: Suppose one is given an at mo…
Given a ring of subsets of a non-empty set, there is a universal measure on the ring with values in an associated complete locally convex space which carries, through its typology, much of the combinatorial and measure theoretic structure of the ring. Moreover, vector measures o…
In this paper we will determine the exact Hausdorff dimension for a wide class of random recursive constructions.
In this memoir, the authors develop a theory of almost periodic measures on a locally compact abelian group [italic]G which includes as special cases the original theory of H. Bohr as well as most of the subsequent generalizations by N. Wiener, V. Stepanov, A. S. Besicovitch, W.…
This paper offers a new tool for the study of complex manifolds--a theory of intrinsic measures on complex manifolds.
This paper is an important treatise on the theory of real functions. It is motivated by a study of Rogers and Taylor characterizing those interval functions which are absolutely continuous with respect to the [italic]s-dimensional Hausdorff measure. This leads naturally to inves…
We present a self-contained account of measure theory and integration in a Banach space. We give a detailed analysis of the weak Baire probabilities on a Banach space E, and on its second dual. Scalarly (= weak) measurable functions valued in E are studied via their image measur…
In this paper measurable selection theory is studied from the modern descriptive set theory point of view.