Basque weak quantifiers optionally agree with the inflected verb in number. This papers’ main aim is to study the dialectal variation shown by this phenomenon. The study will show that it is necessary to differentiate at least three systems: the western-central system, one that we will call the transition system, and the eastern system (souletin). The western-central system allows the presence ...

The intonation of Italian can vary according to pragmatic and sociolinguistic factors. This paper presents an analysis of the localised intonational events conveying the pragmatic meaning of interrogation in two regional varieties of Italian (Rome and Perugia). Data show the type and the distribution of the accents and the boundary occurring in interrogative tone groups selected from map-task d...

Economic models of products sold in the retail channel typically only control for whether a product is available in at least one store in a given market, i.e., variation along the extensive margin. We demonstrate that it is also important to control for intensive margin variation regarding the depth of a product’s availability. Looking at five grocery categories, we show that (a) many products ...

Let X be a given set, and let R, S be some classes of certain subsets of X. We say that R is a ring if A+B ∈ R, A−B ∈ R whenever A ∈ R, B ∈ R. We say that S is a σ-ring if it is a ring and if for every sequence A1, A2, . . ., where Ai ∈ S (i = 1, 2, . . .), the sum ∑∞ i=1 Ai is also contained in S. Let B be a commutative Banach algebra with a unity, i.e. a Banach space, where for all pairs f ∈ ...

In the paper [7], Guasoni studies financial markets which are subject to proportional transaction costs. The standard martingale framework of stochastic finance is not applicable in these markets, since the transaction costs force trading strategies to have bounded variation, while continuoustime martingale strategies have infinite transaction cost. The main question that arises out of [7] is w...

We show that absolutely continuous spectrum of one-dimensional Schrödinger operators may be destroyed by adding to them decaying perturbation potentials of bounded variation.

The Jordan decomposition states that a function f : R → R is of bounded variation if and only if it can be written as the difference of two monotone increasing functions. In this paper we generalize this property to real valued BV functions of many variables, extending naturally the concept of monotone function. Our result is an extension of a result obtained by Alberti, Bianchini and Crippa. A...

We show that for every Lebesgue measurable function f : [0, 1] → R there exists a compact set C of Hausdorff dimension 1/2 such that f is of bounded variation on C, and there exist compact sets Cα of Hausdorff dimension 1−α such that f is Hölder-α on Cα (0 < α < 1). These answer questions of M. Elekes, which were open even for continuous functions f . Our proof goes by defining a discrete Hausd...

A major obstacle in extending the theory of well-bounded operators to cover operators whose spectrum is not necessarily real has been the lack of a suitable variation norm applicable to functions defined on an arbitrary nonempty compact subset σ of the plane. In this paper we define a new Banach algebra BV (σ) of functions of bounded variation on such a set and show that the function theoretic ...

(i) The integral of a non-negative extended real-valued measurabele function f on R d is given by R d f (x)dx = sup g R d g(x)dx where the supremum is taken over all bounded functions 0 ≤ g ≤ f which are bounded and supported on a set of finite measure. (ii) First suppose α < −n, and define a strictly decreasing sequence x m 0. We define step functions g n as follows. Define the sets A m = B xm...