Sentence examples for be a null measure from inspiring English sources

Let be a null measure set, we have to prove that is also a null measure set.

Let us show that is a null measure set.

Therefore and thus is a null measure set.

Since is absolutely continuous on the set is a null measure set for each.

Let us show that the set is a null measure set.

Since contains no positive measure subset we can ensure that is a null measure set for all,, and since increases with and, we conclude that is a null measure set.

Since and are absolutely continuous there is a null measure set such that for all, thus for we have (3.8).

Analogous arguments show that is a null measure set, thus the proof of Claim 3 is complete.

Suppose that there is a null-measure set such that conditions and in Theorem 3.1 hold for and assume moreover that the following condition holds: there exists such that for all,, one has.

Suppose that there is a null-measure set such that conditions and in Theorem 3.1 hold for and assume moreover that the following condition holds: for every there exists such that for all,, and one has.

For every n ∈ N, the set { t ∈ I n : x ( t ) = γ n ( t ) } is a null-measure set, for otherwise we would have in a positive measure set | γ n ″ ( t ) | = | x ″ ( t ) | ≤ M ( t ) (because  x ∈ K ), a contradiction with (C2)∗.