On the sums of functions satisfying the condition \((s_ 1)\). (Q595845)
From MaRDI portal
| This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On the sums of functions satisfying the condition \((s_ 1)\). |
scientific article; zbMATH DE number 2084018
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the sums of functions satisfying the condition \((s_ 1)\). |
scientific article; zbMATH DE number 2084018 |
Statements
On the sums of functions satisfying the condition \((s_ 1)\). (English)
0 references
6 August 2004
0 references
In [Real Anal. Exch. 24, No. 1, 171--183 (1998; Zbl 0940.26003)], the author defined when a function \(f:\mathbb R\to\mathbb R\) satisfies the condition (\(s_1\)), respectively (\(s_2\)). In the present paper he proves the following result: If a function \(f\) is a sum of functions \(g\) and \(h\) having property (\(s_1\)), or if \(f\) has property (\(s_2\)), then there exist Darboux functions \(\phi\) and \(\psi\) with the property (\(s_1\)) such that \(f=\phi+\psi\).
0 references
density topology
0 references
condition \((s_1)\)
0 references
condition \((s_2)\)
0 references
Darboux functions
0 references
generalized continuity
0 references