Ultrafilter extensions of asymptotic density

Grebík, 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 $\{AP\}$(null) and $\{AP\}$(*). 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},
keywords = {asymptotic density; measure; ultrafilter; P-ultrafilter},
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 ${AP}$(null) and ${AP}$(*). We also present a characterization of a $P$- and semiselective ultrafilters using the ultraproduct of $\sigma $-additive measures.
LA - eng
KW - asymptotic density; measure; ultrafilter; P-ultrafilter
UR - http://eudml.org/doc/294375
ER -