Separable σ-Algebra

Separable σ-Algebra

In der Maßtheorie wird eine σ-Algebra als separabel bezeichnet, wenn sie aus einer abzählbaren Anzahl von Mengen erzeugt werden kann.

Beispiel

Die Borel'schen σ-Algebren sind separabel, denn sie werden von den Quadern mit rationalen Endpunkten (a_1,b_1)\times\ldots\times (a_n,b_n) erzeugt.


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