Add to ORKGStatistics requires consideration of the "ideal estimates" defined through the posterior mean of fractional powers of finite measures. In this paper we study L 1=fl , the linear space spanned by flth power of finite measures, fl 2 (0; 1). It is shown that L 1=fl generalizes the Lebesgue function space L 1=fl (¯), and shares most of its important properties: It is a uniformly convex (hence reflexive) Banach space with L 1=(1\Gammafl) as its dual. These results are analogous to classical counterparts but do not require a dominating measure. They also guarantee the unique existence of the ideal estimate. Contents 1 Introduction 4 2 Measure spaces 6 3 Generalized Lebesgue spaces 8 4 Completeness 11 5 Conjugate and Transpose 13 6 Dua...
This paper discusses the concept of a general definition of measure, and shows that the Lebesgue mea...
Abstract. The purpose of this work is to study regularity of So-bolev functions on metric measure sp...
The ultraproducts of measurable linear spaces with probability measure are considered. We study some...
The norm on a Banach space gives rise to a subharmonic function on the complex plane for which the d...
The norm on a Banach space gives rise to a subharmonic function on the complex plane for which the d...
We consider the Banach function spaces, called fully measurable grand Lebesgue spaces, associated wi...
In this paper we characterize the continuous linear sufficient statistics for a dominated collection...
Linear spaces consisting of -finite probability measures and infinite measures (improper priors an...
Majorizing measure techniques are developed and applied to Banach space theory. In particular, the f...
AbstractConsider a generalized random variable X assuming values in a Banach space X with conjugate ...
The Lebesgue property (order-continuity) of a monotone convex function on a solid vec-tor space of m...
In [14] we formalized probability and probability distribution on a finite sample space. In this art...
We prove that if p> 1 and ψ:] 0 , p- 1 [→] 0 , ∞[is nondecreasing, then sup0<1ψ(p-11-logt)‖f∗‖...
The notion of real partit ion introduced in the article presents a convenient tool for transferring ...
This paper contains a complete class theorem (Theorem 3.2) which applies to most statistical estimat...
This paper discusses the concept of a general definition of measure, and shows that the Lebesgue mea...
Abstract. The purpose of this work is to study regularity of So-bolev functions on metric measure sp...
The ultraproducts of measurable linear spaces with probability measure are considered. We study some...
The norm on a Banach space gives rise to a subharmonic function on the complex plane for which the d...
The norm on a Banach space gives rise to a subharmonic function on the complex plane for which the d...
We consider the Banach function spaces, called fully measurable grand Lebesgue spaces, associated wi...
In this paper we characterize the continuous linear sufficient statistics for a dominated collection...
Linear spaces consisting of -finite probability measures and infinite measures (improper priors an...
Majorizing measure techniques are developed and applied to Banach space theory. In particular, the f...
AbstractConsider a generalized random variable X assuming values in a Banach space X with conjugate ...
The Lebesgue property (order-continuity) of a monotone convex function on a solid vec-tor space of m...
In [14] we formalized probability and probability distribution on a finite sample space. In this art...
We prove that if p> 1 and ψ:] 0 , p- 1 [→] 0 , ∞[is nondecreasing, then sup0<1ψ(p-11-logt)‖f∗‖...
The notion of real partit ion introduced in the article presents a convenient tool for transferring ...
This paper contains a complete class theorem (Theorem 3.2) which applies to most statistical estimat...
This paper discusses the concept of a general definition of measure, and shows that the Lebesgue mea...
Abstract. The purpose of this work is to study regularity of So-bolev functions on metric measure sp...
The ultraproducts of measurable linear spaces with probability measure are considered. We study some...