Assertion: set | /r/HasProperty | measurable
Facets:
value: lebesgue
type: DEGREE
Source sentences:
text: One example of a regularity property is the Lebesgue measurability: a set of reals is Lebesgue measurable if it differs from a Borel set by a null set, namely, a set that can be covered by sets of basic open intervals of arbitrarily-small total length.
text: Thus, trivially, every Borel set is Lebesgue measurable, but sets more complicated than the Borel ones may not be.
text: Any set which has a well-defined Lebesgue measure is said to be "measurable", but the construction of the Lebesgue measure (for instance using Carathéodory's extension theorem) does not make it obvious whether non-measurable sets exist.