We present four versions of Egoroff's theorems for measurable closed-valued multifunctions on non-additive measure spaces. The conditions provided for each of these four versions are not only sufficient, but also necessary. In our discussions the continuity of non-additive measures is not required. The previous related results are improved and generalized.
Citation: Tao Chen, Hui Zhang, Jun Li. Egoroff's theorems for random sets on non-additive measure spaces[J]. AIMS Mathematics, 2021, 6(5): 4803-4810. doi: 10.3934/math.2021282
We present four versions of Egoroff's theorems for measurable closed-valued multifunctions on non-additive measure spaces. The conditions provided for each of these four versions are not only sufficient, but also necessary. In our discussions the continuity of non-additive measures is not required. The previous related results are improved and generalized.
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Tao Chen, Hui Zhang, Jun Li. Egoroff's theorems for random sets on non-additive measure spaces[J]. AIMS Mathematics, 2021, 6(5): 4803-4810. doi: 10.3934/math.2021282
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