# On $\mathbb{I}$-approximate limits and $\mathbb{I}$-approximate smoothness

Commentationes Mathematicae (2006)

- Volume: 46, Issue: 1
- ISSN: 2080-1211

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topRafał 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 -

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