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A metric on space of measurable functions and the related convergence. (English) Zbl 1242.28028

Summary: A new metric is proposed on the space of measurable functions in the setting of non-additive measure theory. The convergence induced from the metric can be used to describe the convergence in measure for sequences of measurable functions. Furthermore, the space of measurable functions is complete under the metric.

MSC:

28E10 Fuzzy measure theory
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[1] DOI: 10.1007/978-3-662-03961-8
[2] Bhaskara Rao K. P. S., Theory of Charges (1983) · Zbl 0516.28001
[3] DOI: 10.5802/aif.53 · Zbl 0064.35101
[4] DOI: 10.1007/978-94-017-2434-0
[5] DOI: 10.1002/int.20477 · Zbl 1216.28018
[6] Grabisch M., Fuzzy Measures and Integrals – Theory and Applications (2000) · Zbl 0963.62052
[7] Ha M., Fuzzy Sets and Systems 95 pp 77–
[8] DOI: 10.1016/S0165-0114(97)00395-3 · Zbl 0959.28014
[9] DOI: 10.1016/S0096-3003(01)00317-4 · Zbl 1025.28012
[10] Mesiar R., Kybernetika 46 pp 1098–
[11] DOI: 10.1016/0165-0114(93)90148-B · Zbl 0816.28012
[12] DOI: 10.1016/0165-0114(94)90008-6 · Zbl 0844.28015
[13] DOI: 10.1016/j.ijar.2011.07.004 · Zbl 1244.28021
[14] DOI: 10.1007/s11587-008-0025-x · Zbl 1232.28015
[15] DOI: 10.1016/j.fss.2004.03.022 · Zbl 1059.28016
[16] Takahashi M., RIMS Kokyuroku 1452 pp 11–
[17] DOI: 10.1007/s12190-009-0358-y · Zbl 1210.28028
[18] DOI: 10.1080/03081079708945174 · Zbl 0880.28015
[19] Wang Z., Fuzzy Sets and Systems 16 pp 277–
[20] DOI: 10.1007/978-1-4757-5303-5
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