2018

DOI: 10.1007/s00010-018-0618-8

|View full text |Cite

|

Sign up to set email alerts

|

Variants on the Berz sublinearity theorem

¹

,

Adam Ostaszewski

²

Abstract: To Roy O. Davies on his 90 th birthday.Abstract. We consider variants on the classical Berz sublinearity theorem, using only DC, the Axiom of Dependent Choices, rather than AC, the Axiom of Choice which Berz used. We consider thinned versions, in which conditions are imposed on only part of the domain of the function -results of quantifierweakening type. There are connections with classical results on subadditivity. We close with a discussion of the extensive related literature.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

0

Mentioning

1

Contrasting

0

Year Published

2018

2018

2023

2023

Publication Types

Select...

Article5

Relationship

Self Cite0

Independent5

Authors

Journals

Cited by 5 publications

(1 citation statement)

References 54 publications

Supporting

0

Mentioning

1

Contrasting

0

Order By: Relevance

“…Note that HB for separable normed spaces is not provable from DC [DodM,Cor. 4], unless the space is complete -see [BinO10].…”

Section: Introductionmentioning

confidence: 99%

Set theory and the analyst

¹

,

²

2018

European Journal of Mathematics

View full text Add to dashboard Cite

Then to the rolling heaven itself I cried, Asking what lamp had destiny to guide Her little children stumbling in the dark. And 'A blind understanding' heaven replied.

“…Note that HB for separable normed spaces is not provable from DC [DodM,Cor. 4], unless the space is complete -see [BinO10].…”

Section: Introductionmentioning

confidence: 99%

Set theory and the analyst

¹

,

²

2018

European Journal of Mathematics

View full text Add to dashboard Cite

Then to the rolling heaven itself I cried, Asking what lamp had destiny to guide Her little children stumbling in the dark. And 'A blind understanding' heaven replied.

Further remarks on local K-boundedness of K-subadditive set-valued maps

Jabłońska,

Nikodem

2023

Aequat. Math.

View full text Add to dashboard Cite

Let X be an abelian metric group with an invariant metric, Y be a real normed space and K be a convex cone in Y. We prove that a K-subadditive (K-superadditive) compact- and convex-valued map $$F:X\rightarrow \mathcal{C}\mathcal{C}(Y)$$ F : X → C C ( Y ) , for which the functionals $$f_{y^*}(x)=\inf y^*(F(x))$$ f y ∗ ( x ) = inf y ∗ ( F ( x ) ) are lower (upper, resp.) semicontinuous for any real continuous and non-negative on K functional $$y^*$$ y ∗ , has to be locally K-bounded on X. Our results refer to the papers Banakh and Jabłońska (Israel J Math 230:361–386, 2019), Jabłońska and Nikodem (Math Inequal Appl 22:1081–1089, 2019) and Nikodem (Aequationes Math 62:175–183, 2001).

On Subadditive Functions Bounded Above on a “Large” Set

¹

,

²

,

³

et al. 2020

View full text Add to dashboard Cite

It is well known that boundedness of a subadditive function need not imply its continuity. Here we prove that each subadditive function f : X → R bounded above on a shift-compact (non-Haar-null, non-Haar-meagre) set is locally bounded at each point of the domain. Our results refer to [31, Chapter 16] and papers

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

Product

Browser Extension Assistant by scite Citation Statement Search Reference Check Visualizations Dashboards Explore Journals Explore Organizations Explore Funders Embedding Badge Embedding Citation Search Pricing

Resources

Blog Help & FAQ Accessibility Statement API Terms For Universities & Governments For Researchers For Publishers For Corporate, Pharma & Enterprise Author Marketing Become an Affiliate Get an organization trial or quote scite Data & Services

About

News & Press Careers Read our Paper Coverage

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Copyright © 2024 scite LLC. All rights reserved.

Made with 💙 for researchers

Part of the Research Solutions Family.