Lineability within Peano Curves, Martingales, and Integral Theory
Joint Authors
Bartoszewicz, Artur
Głąb, Szymon
Bienias, Marek
Source
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-12-04
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
This paper is devoted to give several improvements of some known facts in lineability approach.
In particular, we prove that (i) the set of continuous mappings from the unit interval onto the unit square contains a closed, c-semigroupable convex subset, (ii) the set of pointwise convergent martingales (Xn)n∈N with EXn→∞ is c-lineable, (iii) the set of martingales converging in measure but not almost surely is c-lineable, (iv) the set of sequences (Xn)n∈N of independent random variables, with EXn=0, ∑n=1∞var Xn=∞, and the property that (X1+⋯+Xn)n∈N is almost surely convergent, is c-lineable, (v) the set of bounded functions f:[0,1]×[0,1]→R for which the assertion of Fubini’s Theorem does not hold is consistent with ZFC 1-lineable (it is not 2-lineable), (vi) the set of unbounded functions f:[0,1]×[0,1]→R for which the assertion of Fubini’s Theorem does not hold (with infinite integral allowed) is c-lineable but not c+-lineable.
American Psychological Association (APA)
Bartoszewicz, Artur& Bienias, Marek& Głąb, Szymon. 2018. Lineability within Peano Curves, Martingales, and Integral Theory. Journal of Function Spaces،Vol. 2018, no. 2018, pp.1-8.
https://search.emarefa.net/detail/BIM-1186797
Modern Language Association (MLA)
Bartoszewicz, Artur…[et al.]. Lineability within Peano Curves, Martingales, and Integral Theory. Journal of Function Spaces No. 2018 (2018), pp.1-8.
https://search.emarefa.net/detail/BIM-1186797
American Medical Association (AMA)
Bartoszewicz, Artur& Bienias, Marek& Głąb, Szymon. Lineability within Peano Curves, Martingales, and Integral Theory. Journal of Function Spaces. 2018. Vol. 2018, no. 2018, pp.1-8.
https://search.emarefa.net/detail/BIM-1186797
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1186797