We define a class of so-called thinnable ideals I on the positive integers which includes several well-known examples, e.g., the collection of sets with zero asymptotic density, sets with zero logarithmic density, and several summable ideals. Given a sequence (xn) taking values in a separable metric space and a thinnable ideal I, it is shown that the set of I-cluster points of (xn) is equal to the set of I-cluster points of almost all of its subsequences, in the sense of Lebesgue measure. Lastly, we obtain a characterization of ideal convergence, which improves the main result in [15].

Thinnable Ideals and Invariance of Cluster Points

Leonetti P
2018-01-01

Abstract

We define a class of so-called thinnable ideals I on the positive integers which includes several well-known examples, e.g., the collection of sets with zero asymptotic density, sets with zero logarithmic density, and several summable ideals. Given a sequence (xn) taking values in a separable metric space and a thinnable ideal I, it is shown that the set of I-cluster points of (xn) is equal to the set of I-cluster points of almost all of its subsequences, in the sense of Lebesgue measure. Lastly, we obtain a characterization of ideal convergence, which improves the main result in [15].
2018
2018
Asymptotic density; Cluster point; Erdos-Ulam ideal; Ideal convergence.; Logarithmic density; Statistical convergence; Summable ideal; Thinnable ideal
Leonetti, P
File in questo prodotto:
File Dimensione Formato  
Leonetti_Thinnability_2018_02_01.pdf

non disponibili

Tipologia: Versione Editoriale (PDF)
Licenza: Copyright dell'editore
Dimensione 317.17 kB
Formato Adobe PDF
317.17 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2142092
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 11
  • ???jsp.display-item.citation.isi??? 11
social impact