Izvorni znanstveni članak
Uniform density $u$ and $\I_u$-convergence on a big set
Paweł Barbarski
; Institute of Mathematics, University of Gdańsk, Gdańsk, Poland
Rafał Filipów
; Institute of Mathematics, University of Gdańsk, Gdańsk, Poland
Nikodem Mrożek
; Institute of Mathematics, University of Gdańsk, Gdańsk, Poland
Piotr Szuca
; Institute of Mathematics, University of Gdańsk, Gdańsk, Poland
Sažetak
We point out that
$\I_u$-convergence (where $\I_u$ stands for the ideal of uniform density zero sets)
is not equivalent to the convergence on a set from the dual filter.
Moreover, we show that there are bounded sequences which
are not $\I_u$-convergent on any set with a positive uniform density,
i.e.~$\I_u$ does not have the Bolzano-Weierstrass property. We also study relationship
between the Bolzano-Weierstrass property and nonatomic submeasures.
The Borel complexity of the ideal $\I_u$ is determined in the last section.
Ključne riječi
uniform statistical density; statistical density; ideal convergence; Bolzano-Weierstrass property; P-ideal; nonatomic submeasure; Borel set
Hrčak ID:
68629
URI
Datum izdavanja:
10.6.2011.
Posjeta: 1.566 *