Analysis of information sources in references of the Wikipedia article "Separable space" in English language version.
If is a Borel measure on , the measure algebra of is the Boolean algebra of all Borel sets modulo -null sets. If 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 is separable iff this metric space is separable as a topological space.
If is a Borel measure on , the measure algebra of is the Boolean algebra of all Borel sets modulo -null sets. If 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 is separable iff this metric space is separable as a topological space.
If is a Borel measure on , the measure algebra of is the Boolean algebra of all Borel sets modulo -null sets. If 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 is separable iff this metric space is separable as a topological space.