Sentence examples for a holds for from inspiring English sources

Zhou et al. [2] left an open problem whether the case (alpha =gamma) of Theorem A holds for ρ̃-mixing random variables.

A set (Asubseteq mathbb{R}^{n}) is called m-invex with respect to the mapping (eta :A times Atimes (0, 1]rightarrow mathbb{R}^{n}) for some fixed (min (0, 1]) if (mx+lambda eta (y, x, m) in A) holds for all (x, y in A) and (lambda in [0, 1]).

Therefore (a) holds for any.

Assumption (A) holds for a wide class of (not necessarily closed) sets including these classical models.

Setting (G_{n} :=D_{n} cap G), we see that (G_{n}) is open and (Ssubset G_{n}subset G), that is, (a) holds for each (G_{n}).

As cent su ( k ) [ cent su ( k ) ( cent su ( k ) ( A ) ) ] = cent su ( k ) ( A ) holds for any set A, which can also be inferred from [[72], Proposition 6.1.3.1 iii)], we obtain cent su ( k ) ( cent su ( k ) ( g ) ) = g.

For example, in intuitionism every natural number has a prime factorization; there exist computably enumerable sets that are not computable; $(A \vee \neg A)$ holds for all quantifier free statements $A$.

We say that a property holds for △-a.e.

A similar process holds for cognition.

A similar story holds for other commodities.

A similar inequality holds for.