Sentence examples for I almost surely from inspiring English sources

Reader, I almost surely make less money than you do.

I almost surely would have regretted writing the column.

The quantity E[ LR12] is unknown, but under fairly general conditions the sample mean and variance of L R ^ 12, i = log   f ^ 1, i − log   f ^ 2, i converge almost surely to E[ LR12] and Var[ LR12] = σ12.12, where f ^ 1, i = f 1 (y i | x i ; θ ^ 1 ) and θ ^ 1 is the maximum-likelihood estimate of θ1 (Vuong 1989).

Using Corollary 1, we get B σ, K − σ v 4 ( M − K ) N 1 σ P 2 H H H − 2 i, i → 0 almost surely.

A simple incentive mechanism is to simply say that if I cooperate today with others, I should almost surely get help from others tomorrow.

Then { a n X n, n ≥ 1 } is said to obey the general strong law of large numbers (SLLN) with norming constant { b n, n ≥ 1 } if the normed weighted sums 1 b n ∑ i = 1 n a i ( X i − EX i ) → 0 almost surely (a.s).s

As per Theorem 5 iterative application of (93)–(97) yields sequences r i (t), α i (t) and p i (t) such that: (i) The sum utility for the ergodic limits of r i (t) is almost surely within a small constant of optimal; (ii) The power constraint in (27) and the rate constraints in (26) are almost surely satisfied in an ergodic sense.

Using Lemma 4, we get that B σ, K − σ v 4 c 1 c 2 ( 1 + r ) σ P 2 H H H − 1 i, i 2 → 0 almost surely.

(i.e., almost surely).

(i.e., almost surely) is sometimes included in the definition, but our proposed algorithm includes starting points other than the origin.

If the mean of I is not asymptotically stable, then I is not almost surely exponentially stable.