(U\)-topology and \(m\)-topology on the ring of Measurable Functions, generalized and revisited

• Published in: arXiv.org
• Main Authors: Nandi, Pratip, Atasi Deb Ray, Acharyya, Sudip Kumar
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 03.06.2023
• Subjects: Rings (mathematics); Topology

Let \(\mathcal{M}(X,\mathcal{A})\) be the ring of all real valued measurable functions defined over the measurable space \((X,\mathcal{A})\). Given an ideal \(I\) in \(\mathcal{M}(X,\mathcal{A})\) and a measure \(\mu:\mathcal{A}\to[0,\infty]\), we introduce the \(U_\mu^I\)-topology and the \(m_\mu^I...