Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
On the lack of equi-measurability for certain sets of Lebesgue-measurable functions
View through CrossRef
Abstract
Let Ω be a Lebesgue-measurable set in ℝ
n
of finite positive Lebesgue measure. In this note we calculate the lack of equi-measurability of the set Kc
(Ω), c > 0, of all Lebesgue-measurable functions f : Ω → ℝ such that 0 ≤ f ≤ c, a.e. on Ω. From our result we repair a gap in the Example 2.3 of the paper [APPELL, J.—DE PASCALE, E.: Su alcuni parametri connessi con la misura di non compattezza di Hausdorff in spazi di funzioni misurabili, Boll. Un. Mat. Ital. B (6) 3 (1984), 497–515].
Walter de Gruyter GmbH
Title: On the lack of equi-measurability for certain sets of Lebesgue-measurable functions
Description:
Abstract
Let Ω be a Lebesgue-measurable set in ℝ
n
of finite positive Lebesgue measure.
In this note we calculate the lack of equi-measurability of the set Kc
(Ω), c > 0, of all Lebesgue-measurable functions f : Ω → ℝ such that 0 ≤ f ≤ c, a.
e.
on Ω.
From our result we repair a gap in the Example 2.
3 of the paper [APPELL, J.
—DE PASCALE, E.
: Su alcuni parametri connessi con la misura di non compattezza di Hausdorff in spazi di funzioni misurabili, Boll.
Un.
Mat.
Ital.
B (6) 3 (1984), 497–515].
Related Results
On Soft Lebesgue Measure
On Soft Lebesgue Measure
In this article, we introduce the concept of soft intervals, soft ordering and sequences of soft real numbers, and some of their structural properties are studied. The notion of so...
Measure Theory and Lebesgue Integration Theories
Measure Theory and Lebesgue Integration Theories
As discussed in the previous chapter, the fundamental theories of measure and Lebesgue integration are the prerequisites for the formalization of probability theory in higher-order...
Degradation Mechanism of Tungsten Electrode for Fusing Joining
Degradation Mechanism of Tungsten Electrode for Fusing Joining
Lifetime of tungsten electrodes for fusing was investigated in relation to their microstructure. Tungsten electrodes with two types of microstructures (recrystallized equi-axed and...
Uniaxial and Biaxial Mechanical Properties of Porcine Linea Alba
Uniaxial and Biaxial Mechanical Properties of Porcine Linea Alba
Trocar site hernia (or incisional hernia) is a severe complication postlaparoscopic surgery that is commonly associated with the linea alba.However, the few studies on the mechanic...
Multidisciplinary Delphi study validated variables for calculating cost of medication errors in the Sri Lankan context
Multidisciplinary Delphi study validated variables for calculating cost of medication errors in the Sri Lankan context
Introduction
The burden of medication errors needs to be costed but no standard method, nor a standard list of variables, has yet been identified. Hence, this stu...
Fuzzimetric Sets: An Integrated Platform for Both Types of Interval Fuzzy Sets
Fuzzimetric Sets: An Integrated Platform for Both Types of Interval Fuzzy Sets
Type-2 sets are the generalized “fuzzified” sets that can be used in the fuzzy system. Unlike type-1 fuzzy sets, Type-2 allow the fuzzy sets to be “fu...
On Soft Lebesgue Measure
On Soft Lebesgue Measure
In this article, we introduce the concept of soft intervals, soft ordering and sequences of soft real numbers and study their properties and some interesting results. Also the noti...
On Fuzzy γI-Continuity and γI-Irresoluteness via K-Fuzzy γI-Open Sets
On Fuzzy γI-Continuity and γI-Irresoluteness via K-Fuzzy γI-Open Sets
In this article, we explored and investigated a novel class of fuzzy sets, called k-fuzzy γI-open (k-FγI-open) sets in fuzzy ideal topological spaces (FITSs) based on Sostak՚s sens...