0000000000276285
AUTHOR
Caterina Maniscalco
showing 6 related works from this author
A comparison of three recent selection theorems
2007
We compare a recent selection theorem given by Chistyakov using the notion of modulus of variation, with the Schrader theorem based on bounded oscillation and with the Di Piazza-Maniscalco theorem based on bounded ${\cal A},\Lambda$-oscillation.
A Structural Theorem for Metric Space Valued Mappings of Φ-bounded Variation
2009
In this paper we introduce the notion of $\Phi$-bounded variation for metric space valued mappings defined on a subset of the real line. Such a notion generalizes the one for real functions introduced by M. Schramm, and many previous generalized variations. We prove a structural theorem for mappings of $\Phi$-bounded variation. As an application we show that each mapping of $\Phi$-bounded variation defined on a subset of $\mathbb{R}$ possesses a $\Phi$-variation preserving extension to the whole real line.
A pointwise selection principle for metric semigroup valued functions
2008
Abstract Let ∅ ≠ T ⊂ R , ( X , d , + ) be an additive commutative semigroup with metric d satisfying d ( x + z , y + z ) = d ( x , y ) for all x , y , z ∈ X , and X T the set of all functions from T into X . If n ∈ N and f , g ∈ X T , we set ν ( n , f , g , T ) = sup ∑ i = 1 n d ( f ( t i ) + g ( s i ) , g ( t i ) + f ( s i ) ) , where the supremum is taken over all numbers s 1 , … , s n , t 1 , … , t n from T such that s 1 ⩽ t 1 ⩽ s 2 ⩽ t 2 ⩽ ⋯ ⩽ s n ⩽ t n . We prove the following pointwise selection theorem: If a sequence of functions { f j } j ∈ N ⊂ X T is such that the closure in X of the set { f j ( t ) } j ∈ N is compact for each t ∈ T , and lim n → ∞ ( 1 n lim N → ∞ sup j , k ⩾ N , j…
VARIANTS OF A SELECTION PRINCIPLE FOR SEQUENCES OF REGULATED AND NON-REGULATED FUNCTIONS
2008
Let $T$ be a nonempty subset of $\RB$, $X$ a metric space with metric $d$ and $X^T$ the set of all functions mapping $T$ into $X$. Given $\vep>0$ and $f\in X^T$, we denote by $N(\vep,f,T)$ the least upper bound of those $n\in\NB$, for which there exist numbers $s_1,\dots,s_n,t_1,\dots,t_n$ from $T$ such that $s_1\vep$ for all $i=1,\dots,n$ ($N(\vep,f,T)=0$ if there are no such $n$'s). The following pointwise selection principle is proved: {\em If a sequence of functions\/ $\{f_j\}_{j=1}^\infty\subset X^T$ is such that the closure in $X$ of the sequence\/ $\{f_j(t)\}_{j=1}^\infty$ is compact for each $t\in T$ and\/ $\limsup_{j\to\infty}N(\vep,f_j,T)0$, then\/ $\{f_j\}_{j=1}^\infty$ contains …
A pointwise selection principle for metric semigoup valued functions
2008
Let $\emptyset\neq T \subset \RB, \hspace{.1in} (X,d,+)$ be an additive commutative semigroup with metric $d$ satisfying $d(x+z,y+z)=d(x,y)$ for all $x,y,z \in X,$ and $X^T$ the set of all functions from $T$ into $X$. If $n \in \NB$ and $f,g \in X^T$, we set $\nu (n,f,g,T) = \sup \sum _{i=1} ^{n} d(f(t_i)+g(s_i), g(t_i)+f(s_i))$, where the supremum is taken over all numbers $s_1,...,s_n,t_1,....,t_n$ from $T$ such that $s_1 \leq t_1 \leq s_2 \leq t_2 \leq ...\leq s_n \leq t_n.$ We prove the following pointwise selection theorem: \textit{If a sequence of functions $\{f_j\}_{j \in \NB} \subset X^T$ is such that the closure in $X$ of the set $\{f_j(t)\}_{j \in \NB}$ is compact for each t \in T…
ISODECIMAL NUMBERS
2006
The aim of this paper is to investigate pairs of real numbers of the type $(x,\frac{1}{x}),$ \ $(x,\frac{a}{x})$ and $(x,x^{2}),$ where the first component is a real number $x\neq0$ and the fractional parts of the coordinates are equal. We call such numbers \textit{isodecimal}.