Geodesic
Minimality of Convergence in Measure Topologies on Finite von Neumann Algebras
Matematičeskie zametki, Tome 75 (2004) no. 3, pp. 342-349

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We prove that the natural embedding of the metric ideal space on a finite von Neumann algebra ${\mathscr M}$ into the $*$-algebra of measurable operators $\widetilde {\mathscr M}$ endowed with the topology of convergence in measure is continuous. Using this fact, we prove that the topology of convergence in measure is a minimal one among all metrizable topologies consistent with the ring structure on $\widetilde {\mathscr M}$. 
@article{MZM_2004_75_3_a1,
     author = {A. M. Bikchentaev},
     title = {Minimality of {Convergence} in {Measure} {Topologies} on {Finite} von {Neumann} {Algebras}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {342--349},
     publisher = {mathdoc},
     volume = {75},
     number = {3},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_75_3_a1/}
}
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A. M. Bikchentaev. Minimality of Convergence in Measure Topologies on Finite von Neumann Algebras. Matematičeskie zametki, Tome 75 (2004) no. 3, pp. 342-349. http://geodesic.mathdoc.fr/item/MZM_2004_75_3_a1/