On $𝕀$-approximate limits and $𝕀$-approximate smoothness

Rafał Zduńczyk. "On $\mathbb {I}$-approximate limits and $\mathbb {I}$-approximate smoothness." Commentationes Mathematicae 46.1 (2006): null. <http://eudml.org/doc/291586>.

@article{RafałZduńczyk2006,
abstract = {In this paper we present some results based on slightly modified idea of the $\mathbb \{I\}$-density introduced by Władysław Wilczyński. Some theorems are generalized versions of results from [2] and [3]. We investigate properties of functions from $\mathbb \{R\}^X$, where $X$ is supplied with the $\mathbb \{I\}$-density. We try to free our considerations from the assumption of Baire property, or measurability. In some cases this is not done yet. Star-marked statements still need that assumption, proofs presented here are done for Baire property, but it is possible to adapt them to measure. $\mathbb \{I\}$-density itself does not require any structure of considered space but a metric vector space over $\mathbb \{R\}$. However, in last section we confine ourselves to $\mathbb \{R\}$, for we make use of $\mathbb \{R\}$’s structure for simplicity. To find more about related topics see [4], [5], more bibliography one can find in [1] and [5].},
author = {Rafał Zduńczyk},
journal = {Commentationes Mathematicae},
keywords = {Density point; algebra of sets; generalized derivative},
language = {eng},
number = {1},
pages = {null},
title = {On $\mathbb \{I\}$-approximate limits and $\mathbb \{I\}$-approximate smoothness},
url = {http://eudml.org/doc/291586},
volume = {46},
year = {2006},
}

TY - JOUR
AU - Rafał Zduńczyk
TI - On $\mathbb {I}$-approximate limits and $\mathbb {I}$-approximate smoothness
JO - Commentationes Mathematicae
PY - 2006
VL - 46
IS - 1
SP - null
AB - In this paper we present some results based on slightly modified idea of the $\mathbb {I}$-density introduced by Władysław Wilczyński. Some theorems are generalized versions of results from [2] and [3]. We investigate properties of functions from $\mathbb {R}^X$, where $X$ is supplied with the $\mathbb {I}$-density. We try to free our considerations from the assumption of Baire property, or measurability. In some cases this is not done yet. Star-marked statements still need that assumption, proofs presented here are done for Baire property, but it is possible to adapt them to measure. $\mathbb {I}$-density itself does not require any structure of considered space but a metric vector space over $\mathbb {R}$. However, in last section we confine ourselves to $\mathbb {R}$, for we make use of $\mathbb {R}$’s structure for simplicity. To find more about related topics see [4], [5], more bibliography one can find in [1] and [5].
LA - eng
KW - Density point; algebra of sets; generalized derivative
UR - http://eudml.org/doc/291586
ER -