Ultrafilter extensions of asymptotic density
Commentationes Mathematicae Universitatis Carolinae (2019)
- Volume: 60, Issue: 1, page 25-37
- ISSN: 0010-2628
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topGrebík, Jan. "Ultrafilter extensions of asymptotic density." Commentationes Mathematicae Universitatis Carolinae 60.1 (2019): 25-37. <http://eudml.org/doc/294375>.
@article{Grebík2019,
abstract = {We characterize for which ultrafilters on $\omega$ is the ultrafilter extension of the asymptotic density on natural numbers $\sigma$-additive on the quotient boolean algebra $\mathcal\{P\}(\omega)/d_\{\mathcal\{U\}\}$ or satisfies similar additive condition on $\mathcal\{P\}(\omega)/\text\{fin\}$. These notions were defined in [Blass A., Frankiewicz R., Plebanek G., Ryll-Nardzewski C., \{A Note on extensions of asymptotic density\}, Proc. Amer. Math. Soc. \{129\} (2001), no. 11, 3313--3320] under the name $\{\boldsymbol\{AP\}\}$(null) and $\{\boldsymbol\{AP\}\}$(*). We also present a characterization of a $P$- and semiselective ultrafilters using the ultraproduct of $\sigma$-additive measures.},
author = {Grebík, Jan},
journal = {Commentationes Mathematicae Universitatis Carolinae},
language = {eng},
number = {1},
pages = {25-37},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Ultrafilter extensions of asymptotic density},
url = {http://eudml.org/doc/294375},
volume = {60},
year = {2019},
}
TY - JOUR
AU - Grebík, Jan
TI - Ultrafilter extensions of asymptotic density
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2019
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 60
IS - 1
SP - 25
EP - 37
AB - We characterize for which ultrafilters on $\omega$ is the ultrafilter extension of the asymptotic density on natural numbers $\sigma$-additive on the quotient boolean algebra $\mathcal{P}(\omega)/d_{\mathcal{U}}$ or satisfies similar additive condition on $\mathcal{P}(\omega)/\text{fin}$. These notions were defined in [Blass A., Frankiewicz R., Plebanek G., Ryll-Nardzewski C., {A Note on extensions of asymptotic density}, Proc. Amer. Math. Soc. {129} (2001), no. 11, 3313--3320] under the name ${\boldsymbol{AP}}$(null) and ${\boldsymbol{AP}}$(*). We also present a characterization of a $P$- and semiselective ultrafilters using the ultraproduct of $\sigma$-additive measures.
LA - eng
UR - http://eudml.org/doc/294375
ER -
References
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