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...
A note on linear compositions of the Mellin convolution operators in the weighted Mellin-Lebesgue spaces
A note on linear compositions of the Mellin convolution operators in the weighted Mellin-Lebesgue spaces
Abstract
In this article, we express a numerical form of the convergence using the suitable modulus of smoothness for linear compositions of ...
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...
Notes on noncommutative LP and Orlicz spaces
Notes on noncommutative LP and Orlicz spaces
Since the pioneering work of Dixmier and Segal in the early 50’s, the theory of noncommutative LP-spaces has grown into a very refined and important theory with wide applications. ...
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...
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...
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...