Classifier Instance:

Anchor text: σ-algebra
Target Entity: Sigma\u002dalgebra
Preceding Context: To qualify as a measure (see Definition below), a function that assigns a non-negative real number or +∞ to a set's subsets must satisfy a few conditions. One important condition is countable additivity. This condition states that the size of the union of a sequence of disjoint subsets is equal to the sum of the sizes of the subsets. However, it is in general impossible to associate a consistent size to each subset of a given set and also satisfy the other axioms of a measure. This problem was resolved by defining measure only on a sub-collection of all subsets; the subsets on which the measure is to be defined are called measurable and they are required to form a
Succeeding Context: , meaning that unions, intersections and complements of sequences of measurable subsets are measurable. Non-measurable sets in a Euclidean space, on which the Lebesgue measure cannot be defined consistently, are necessarily complicated, in the sense of being badly mixed up with their complements; indeed, their existence is a non-trivial consequence of the axiom of choice.
Paragraph Title: null
Source Page: Measure (mathematics)

Ground Truth Types:

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Predicted Types:

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yagoGeoEntity-1.2592758220924725 0
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