Sentence examples for array of constants from inspiring English sources

Let,, be an array of constants such that.

Let, be a sequence of random variables and let, be an array of constants.

Let be a random variable and be an array of constants satisfying (1.10),.

(iv) The concept of residually ( r, h ) -integrable concerning the array of constants { a n i } is strictly weaker than the concept of h-integrable concerning the array of constants { a n i } and h-integrable with exponent r.  .

Let { a n i, i ≥ 1, n ≥ 1 } be an array of constants satisfying (1.1) and (3.7).

Let be a sequence of identically distributed -mixing random variables, and let be an array of constants satisfying (110).

Ordóñez Cabrera [3] introduced the concept of uniform integrability concerning an array of constant weights.

Ordóñez Cabrera and Volodin [6] introduced the notion of h-integrability for an array of random variables concerning an array of constant weights, and proved that this concept is weaker than Cesàro uniform integrability, { a n i } -uniform integrability and Cesàro α-integrability.

The residual ( 1, h ) -integrability concerning the arrays of constants was defined by Yuan and Tao [9], who called it the residual h-integrability, and was extended by Ordóñez Cabrera et al. [10] to the conditionally residually h-integrability relative to a sequence of σ-algebras.

random variables satisfying, and let be an array of real constants such that (1.5).

and let { a n i ; 1 ≤ i ≤ n, n ≥ 1 } be an array of real constants such that (1.1) satisfies for α ∈ ( 0, 2 ).