On some properties of Hamel bases and their applications to Marczewski measurable functions

• Autorzy: François Dorais , Rafał Filipów , Tomasz Natkaniec
• Języki publikacji: EN

Abstrakty

EN

We introduce new properties of Hamel bases. We show that it is consistent with ZFC that such Hamel bases exist. Under the assumption that there exists a Hamel basis with one of these properties we construct a discontinuous and additive function that is Marczewski measurable. Moreover, we show that such a function can additionally have the intermediate value property (and even be an extendable function). Finally, we examine sums and limits of such functions.

Słowa kluczowe

EN

Linear function; Additive function; (s)-measurable set; Marczewski measurable set; (s)-measurable function; Marczewski measurable function; The intermediate value property; Darboux function; Connectivity function; Extendable function; Covering Property Axiom

Kategorie tematyczne

• 28A20: Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
• 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.)
• 26A51: Convexity, generalizations
• 03E35: Consistency and independence results

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 3
• Strony: 487-508

Daty

wydano

2013-03-01

online

2012-12-22

Twórcy

autor

François Dorais

• Department of Mathematics, University of Michigan, 2074 East Hall, 530 Church Street, Ann Arbor, MI, 48109-1043, USA

autor

Rafał Filipów

• Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952, Gdańsk, Poland

autor

Tomasz Natkaniec

• Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952, Gdańsk, Poland

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Identyfikatory

DOI

10.2478/s11533-012-0144-1