A novel structure for measurable functions sequence convergence based on approach measure space

Ali  A. Hammood; Arkan   J. Mohammed; Boushra   Y. Hussein

doi:10.47831/mjpas.v4i3.539

Authors

Ali A. Hammood Department of Mathematics, College of Science, University of Mustansiriyah
Arkan J. Mohammed Department of Mathematics, College of Science, University of Mustansiriyah
Boushra Y. Hussein Department of Mathematics, College of Education, University of Al-Qadisiyah

DOI:

https://doi.org/10.47831/mjpas.v4i3.539

Keywords:

: Almost bounded with respect approach measure, Approach measure space, Approach space, Convergence in approach measure

Abstract

In measure theory, there are several types of convergence of sequences like convergence in
measure, almost everywhere and almost uniformly we presented definition of approach
measure and approach measurable functions also we defined new concepts which
convergence of sequences of approach measurable functions almost everywhere with
respect approach measure and convergence of sequences of approach measurable functions
in approach measure , we studied the relationship between them, We also raised the topic of
"almost bounded" and what its relationship to "bounded"? We will discuss the relation
between uniform convergence and convergence of sequences of approach measurable
functions in approach measure, the relation between convergence of sequences of approach
measurable functions almost everywhere with respect approach measure and convergence of
sequences of approach measurable functions in approach measure.