Sentence examples for countable union from inspiring English sources

We need at least T to be countably Lipschitz, i.e. (Omega ) may be written as a countable union of measurable sets ((Omega _i)_{ige 0}) with (Omega _0) negligible and Open image in new window Lipschitz continuous for every (ige 1).

In addition the metric singularities are precisely given by a countable union of analytic subvarieties.

A countable union of pluripolar sets is pluripolar.

A set of reals is meager iff it is the countable union of nowhere dense sets.

In other words, if {Ai} ⊆ Σ is countable, the countable union ∪Ai is in Σ.

Then (mathcal{X} ) is not the countable union of nowhere dense closed sets.

The polynomial operations on sets (without power) are also continuous: they preserve countable unions of sets.

We show that ({text {Conv}}(mathbb {P}^{n})) contains projective hulls of compact pluripolar sets and countable unions of projective varieties.

For many applications, it is useful to assume that the domain has the form of a sigma-field, which means that it is closed under countable unions and intersections.

For each ordinal α such that 0 < α < ω1, recursively define Σ̰0α to consist of the sets that are countable unions of sets appearing in some Π̰0β, for β < α, and define Π̰0α to consist of the sets that are countable intersections of sets appearing in some Σ̰0β, for β < α.

Remark 2.6 Note that the conditions of A 0 n, A n, n ∈ Z 0 + being closed and the infinite countable unions ⋃ n = 0 ∞ A 0 n and ⋃ n = 0 ∞ A n being closed can be relaxed in Theorem 2.5 (property (i)) to the closeness of the sets A 0 n, A n, n ( ≥ m ) ∈ Z 0 + and ⋃ n = m ∞ A 0 n and ⋃ n = m ∞ A n for some m ∈ Z 0 + being closed while keeping the corresponding result.