<abstract xmlns="http://www.w3.org/1999/xhtml"><p> This note is closely related to the paper [R. Pinciroli: <italic>On the</italic><italic>independence of a generalized statement of Egoroff’s theorem from ZFC after</italic><italic>T. Weiss, </italic>Real Anal. Exchange <bold>32 </bold>(2006-2007), 225-232] and it presents slight improvements of its results. Theorem 1.13 shows a connection with Galois-Tukey embeddings; Corollary 1.14 presents another inequality which is dual to the previously known one; Corollary 3.5 shows that there is no distinction between positive outer measure and full outer measure in the given context; and Corollary 4.3 unifies the known counterexamples.</p></abstract>

This note is closely related to the paper [R. Pinciroli: On theindependence of a generalized statement of Egoroff’s theorem from ZFC afterT. Weiss, Real Anal. Exchange 32 (2006-2007), 225-232] and it presents slight improvements of its results. Theorem 1.13 shows a connection with Galois-Tukey embeddings; Corollary 1.14 presents another inequality which is dual to the previously known one; Corollary 3.5 shows that there is no distinction between positive outer measure and full outer measure in the given context; and Corollary 4.3 unifies the known counterexamples.

Generalized Egoroff’s theorem

Mathematical Institute Slovak Academy of Sciences Jesenn´a 5 SK–041-54 Koˇsice SLOVAKIA

Department of Computer Science Faculty of Science P. J. ˇSaf´arik University Jesenn´a 5 SK–041-54 Koˇsice SLOVAKIA URL: kosice.upjs.sk/˜repicky

Tatra Mountains Mathematical Publications

{"article-title":"Generalized Egoroff\u2019s theorem"}

This note is closely related to the paper [R. Pinciroli: On theindependence of a generalized statement of Egoroff’s theorem from ZFC afterT. Weiss, Real Anal....

Generalized Egoroff’s theorem

Online veröffentlicht: 12. Nov. 2012

Seitenbereich: 81 - 96

DOI: https://doi.org/10.2478/v10127-009-0049-y

Schlüsselwörter
Egoroff’s theorem, measure, category, cardinal invariants, Galois-Tukey embeddings.

This content is open access.

Generalized Egoroff’s theorem

Online veröffentlicht: 12. Nov. 2012

Seitenbereich: 81 - 96

DOI: https://doi.org/10.2478/v10127-009-0049-y

SchlüsselwörterEgoroff’s theorem, measure, category, cardinal invariants, Galois-Tukey embeddings.

This content is open access.

Schlüsselwörter
Egoroff’s theorem, measure, category, cardinal invariants, Galois-Tukey embeddings.