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A relationship between intersection conditions and porosity conditions for local systems. (English) Zbl 0793.26007
In this paper the author proves that if a local system $$\mathbb{S}$$ fulfils the conditions: 1. $$\mathbb{S}(x)= \{x+ S;\;S\in\mathbb{S}(0)\}$$ for every $$x$$, 2. $$S^ +\cup- S^ +\in\mathbb{S}(0)$$ and $$S^ -\cup- S^ -\in \mathbb{S}(0)$$ whenever $$S\in\mathbb{S}(0)$$, 3. If $$\mathbb{S}$$ satisfies the parametric intersection condition, then, for any $$x\in\mathbb{R}$$ and $$S\in \mathbb{S}(x)$$, $p^ +(S,x)\leq {(1/2)+\lambda\over 1+\lambda}\quad\text{and}\quad p^ -(S,x)\leq {(1/2)+\lambda\over 1+\lambda}$ (i.e., the porosity of sets from $$\mathbb{S}(x)$$ at $$x$$ cannot be too large).
Reviewer: R.Pawlak (Łódź)
##### MSC:
 26A21 Classification of real functions; Baire classification of sets and functions
##### Keywords:
local system; parametric intersection condition; porosity
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##### References:
 [1] THOMSON B. S.: Real Functions. Springer-Verlag, 1985. · Zbl 0581.26001
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