7 In this paper, we show that weakly null-additive fuzzy measures on metric spaces possess regularity. Lusin’s theorem, which is well-known in classical measure theory, is generalized to fuzzy measure space by using the 9 regularity and weakly null-additivity. A version of Egoro2’s theorem for the fuzzy measure de3ned on metric spaces is given. An application of Lusin’s theorem to approximation...

Abstract: Let m : Σ → X be a Banach space valued countably additive vector measure. In this paper we present a procedure to construct an m -orthogonal system in the space L(m) of square integrable functions with respect to m . If the vector measure is constructed from a family of indeterminate scalar measures, it is possible to obtain a family of polynomials that is orthogonal with respect to t...

Life-course research has linked childhood experiences to adult mental illness, but most studies focus on anxiety or depressive symptoms, which may be transient. Therefore, this study investigates whether childhood misfortune is associated with taking psychotropic medication, a measure reflecting an underlying chronic mental disorder. Data are from three waves of a national survey of 2,999 U.S. ...

Motivated by the recent results on topology determined by the Sugeno and Choquet integrals we study the topology on the space of measurable functions for a non-additive measure, which is determined by the integral IS based on a semicopula S. We define a family of mappings ρS on the set of measurable functions parameterized by a semicopula S and study their properties. We show that for a semicop...

In this paper we propose a model of …nancial markets in which agents have limited ability to trade and no probability is given from the outset. In the absence of arbitrage opportunities, assets are priced according to a probability measure that lacks countable additivity. Despite …nite additivity, we obtain an explicit representation of the expected value with respect to the pricing measure, ba...

We study the suitability of the additive lagged-Fibonacci pseudorandom number generator for parallel computation. This generator has a relatively short period with respect to the size of its seed. However, the short period is more than made up for with the huge number of full-period cycles it contains. We call these diierent full-period cycles equivalence classes. We show how to enumerate the e...

A typological model of shyness as neurotic-introversion has been suggested but never evaluated. We compared the ability of two direct measures of trait-shyness (Revised Shyness scale, Social Anxiety scale) and two typological measures (additive and interactive versions of neurotic-introversion) to predict peer-rated shyness and talk-time in leaderless groups. One hundred and twenty participants...

This study proposes a new decomposition method that permits a difference in an aggregate measure at a final time point to be split into additive components corresponding to the initial differences in the event rates of the measure and differences in trends in these underlying event rates. For instance, when studying divergence in life expectancy, this method allows researchers to more easily co...

The present paper deals with the study of the notion of an atom of a function m defined on an effect algebra L with values in [0,∞]; a few examples of atoms for null-additive as well as for non-null-additive functions are also given. We have proved a Saks type decomposition theorem for an element a with m(a) > 0 (for a suitable m), which does not contain any atom of m, in a σ-complete effect al...