Separable space (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Separable space" in English language version.

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Džamonja, Mirna; Kunen, Kenneth (1995). "Properties of the class of measure separable compact spaces" (PDF). Fundamenta Mathematicae: 262. arXiv:math/9408201. Bibcode:1994math......8201D. If $\mu$ is a Borel measure on $X$ , the measure algebra of $(X,\mu )$ is the Boolean algebra of all Borel sets modulo $\mu$ -null sets. If $\mu$ is finite, then such a measure algebra is also a metric space, with the distance between the two sets being the measure of their symmetric difference. Then, we say that $\mu$ is separable iff this metric space is separable as a topological space.

Džamonja, Mirna; Kunen, Kenneth (1995). "Properties of the class of measure separable compact spaces" (PDF). Fundamenta Mathematicae: 262. arXiv:math/9408201. Bibcode:1994math......8201D. If $\mu$ is a Borel measure on $X$ , the measure algebra of $(X,\mu )$ is the Boolean algebra of all Borel sets modulo $\mu$ -null sets. If $\mu$ is finite, then such a measure algebra is also a metric space, with the distance between the two sets being the measure of their symmetric difference. Then, we say that $\mu$ is separable iff this metric space is separable as a topological space.

Džamonja, Mirna; Kunen, Kenneth (1995). "Properties of the class of measure separable compact spaces" (PDF). Fundamenta Mathematicae: 262. arXiv:math/9408201. Bibcode:1994math......8201D. If $\mu$ is a Borel measure on $X$ , the measure algebra of $(X,\mu )$ is the Boolean algebra of all Borel sets modulo $\mu$ -null sets. If $\mu$ is finite, then such a measure algebra is also a metric space, with the distance between the two sets being the measure of their symmetric difference. Then, we say that $\mu$ is separable iff this metric space is separable as a topological space.