scholarly journals Generalization and new proof for almost everywhere convergence to imply local convergence in measure

2021 ◽  
pp. 1-5
Author(s):  
Yu-Lin Chou
Keyword(s):  
Local Convergence ◽  
Almost Everywhere Convergence ◽  
Convergence In Measure ◽  
Almost Everywhere

scholarly journals A note on convergence in measure and selection principles

Filomat ◽  
2012 ◽  
Vol 26 (3) ◽  
pp. 473-477
Author(s):  
Dragan Djurcic ◽  
Ljubisa Kocinac
Keyword(s):  
Uniform Convergence ◽  
Almost Everywhere Convergence ◽  
Convergence In Measure ◽  
Mean Convergence ◽  
Measurable Functions ◽  
Almost Everywhere ◽  
Selection Principles ◽  
Almost Uniform Convergence ◽  
Special Modes

It is proved that some classes of sequences of measurable functions satisfy certain selection principles related to special modes of convergence (convergence in measure, almost everywhere convergence, almost uniform convergence, mean convergence).

VMO Space Associated with Parabolic Sections and its Application

2015 ◽  
Vol 58 (3) ◽  
pp. 507-518
Author(s):  
Ming-Hsiu Hsu ◽  
Ming-Yi Lee
Keyword(s):  
Hardy Space ◽  
Weak Convergence ◽  
Bounded Sequence ◽  
Almost Everywhere Convergence ◽  
Almost Everywhere

AbstractIn this paper we define a space VMO𝒫 associated with a family 𝒫 of parabolic sections and show that the dual of VMO𝒫 is the Hardy space . As an application, we prove that almost everywhere convergence of a bounded sequence in implies weak* convergence

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