Some laws of large numbers for arrays of random upper semicontinuous functions

2021 ◽  
Author(s):  
Duong Xuan Giap ◽  
Nguyen Van Quang ◽  
Bui Nguyen Tram Ngoc
Keyword(s):  
Laws Of Large Numbers ◽  
Upper Semicontinuous ◽  
Upper Semicontinuous Functions ◽  
Large Numbers ◽  
Semicontinuous Functions

A method to derive strong laws of large numbers for random upper semicontinuous functions

2001 ◽  
Vol 53 (3) ◽  
pp. 269-275 ◽  
Author(s):  
Ana Colubi ◽  
J. Santos Domı́nguez-Menchero ◽  
Miguel López-Dı́az ◽  
Ralf Körner
Keyword(s):  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Upper Semicontinuous ◽  
Upper Semicontinuous Functions ◽  
Large Numbers ◽  
Semicontinuous Functions

Real Functions, Covers and Bornologies

2021 ◽  
Vol 78 (1) ◽  
pp. 199-214
Author(s):  
Lev Bukovský
Keyword(s):  
Topological Space ◽  
Pointwise Convergence ◽  
Continuous Functions ◽  
Upper Semicontinuous ◽  
Upper Semicontinuous Functions ◽  
Covering Properties ◽  
Real Functions ◽  
Topology Of Pointwise Convergence ◽  
Semicontinuous Functions

Abstract The paper tries to survey the recent results about relationships between covering properties of a topological space X and the space USC(X) of upper semicontinuous functions on X with the topology of pointwise convergence. Dealing with properties of continuous functions C(X), we need shrinkable covers. The results are extended for A-measurable and upper A-semimeasurable functions where A is a family of subsets of X. Similar results for covers respecting a bornology and spaces USC(X) or C(X) endowed by a topology defined by using the bornology are presented. Some of them seem to be new.

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