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All Journal Journal of the Indonesian Mathematical Society Jurnal Eurekamatika
Masta, Al Azhary
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A Note on Inclusion Properties of Weighted Orlicz Spaces Masta, Al Azhary; -, Ifronika; Taqiyuddin, Muhammad
Journal of the Indonesian Mathematical Society Volume 26 Number 1 (March 2020)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.26.1.816.128-136

Abstract

In this paper we present sufficient and necessary conditions for the inclusion relationbetween two weighted Orlicz spaces which complete the Osan\c{c}liol result in 2014.One of the keys to prove our results is to use the norm of the characteristic functionsof the balls in $\mathbb{R}^n$.
KEKONVERGENAN DALAM RUANG LEBESGUE LEMAH DAN EKUIVALENSINYA DENGAN KEKONVERGENAN DALAM RUANG LEBESGUE Amalina, Dina Nur; Sumiaty, Encum; Masta, Al Azhary
Jurnal EurekaMatika Vol 6, No 2 (2018): Jurnal EurekaMatika
Publisher : Mathematics Program Study, Universitas Pendidikan Indonesia (UPI)

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (323.595 KB) | DOI: 10.17509/jem.v6i2.14847

Abstract

ABSTRAK. Ruang Lebesgue lemah merupakan perluasan dari ruang Lebesgue. Ruang ini adalah ruang quasi-norm dengan dilengkapi suatu quasi-norm. Dalam tulisan ini, penulis memperlihatkan kekonvergenan dalam ruang Lebesgue lemah ekuivalen dengan kekonvergenan dalam ruang Lebesgue. Sebagai ruang yang dilengkapi dengan quasi-norm dan memiliki kriteria Cauchy, ruang Lebesgue dapat disebut sebagai ruang quasi-Banach. Kata kunci: Ruang Lebesgue, ruang Lebesgue lemah, quasi-norm, ruang quasi-Banach, kekonvergenan. ABSTRACT. The weak Lebesgue space is an extension of the Lebesgue space. This space is quasi-norm space equipped with a quasi-norm. In this paper, writer show convergence in weak Lebesgue space is equivalent to convergence in Lebesgue space. As a space furnished with quasi-norm and Cauchy’s criteria, the weak Lebesgue space can be referred to as quasi-Banach space. Keywords: Lebesgue space, weak Lebesgue space, quasi-norm, quasi-Banach space, convergence.
Co-Authors -, Ifronika Amalina, Nur Dina Encum Sumiaty, Encum Muhammad Taqiyuddin