Sentence examples for arrays of constants from inspiring English sources

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.

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).

The notion of h-integrability for an array of random variables concerning an array of constants { a n k } is as follows.

Let ({X, X_{n}, ngeq1}) be a sequence of random variables and ({a_{ni}, 1leq ileq n, ngeq1}) be an array of constants.

Theorem D. Let be a sequence of identically distributed NA random variables, and let be an array of constants satisfying (17).

Let { a n i, i ≥ 1, n ≥ 1 } be an array of constants such that sup i ≥ 1 | a n i | = O ( n − r ) for some r > 0 (3.1).