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In this chapter we define the Henstock-Orlicz class for bounded measurable functions with compact support and discuss some fundamental results of this class. Further, we construct H-Orlicz spaces. Several fundamental properties of H-Orlicz space have been discussed. Lastly we prove \(C_0^\infty \) is a dense subset of H-Orlicz space.

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Henstock-Orlicz Spaces and Denseness of \(C_0^{ \infty }\)

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  • 发表日期：

    2025年

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  • Bipan Hazarika,
  • Hemanta Kalita

摘要

In this chapter we define the Henstock-Orlicz class for bounded measurable functions with compact support and discuss some fundamental results of this class. Further, we construct H-Orlicz spaces. Several fundamental properties of H-Orlicz space have been discussed. Lastly we prove \(C_0^\infty \) is a dense subset of H-Orlicz space.