SIFAT INVARIAN TRANSLASI TOPOLOGI KONVERGENSI SERAGAM HAMPIR DIMANA-MANA PADA RUANG FUNGSI TERUKUR
Abstract
The space of functions that is often studied is the space of functions whose members are all measurable functions. One of the methods to study the space is by forming a topology. The problem is how to construct a topology on that function space. In this paper, a topology on the space of equivalent class of measurable functions will be constructed by building a local basis. The local basis of zero functions is used to define open sets in the space. This construction yields results that a topology can be constructed on the space. The resulting topology has the properties of being invariant under translation and being Hausdorff. Furthermore, convergence in that topological space is equivalent to almost everywhere uniform convergence.
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DOI: https://doi.org/10.20527/epsilon.v20i1.16747
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