Sentence examples for countable chain from inspiring English sources

we denote a countable chain.

A is said to be a countable chain if A is a chain and is countable.

We assert that every countable chain of (mathscr{P}) has a supremum in (mathscr{P}).

In fact, if (mathscr{C}={A_{1},A_{2},ldots}) is a countable chain of (mathscr{P}), then (A_{k}) is a countable subset of S for (k=1,2,ldots) .

Recently, Yang [5] have studied some strong limit theorems for countable homogeneous Markov chains indexed by a homogeneous tree and the strong law of large numbers and the AEP for finite homogeneous Markov chains indexed by a homogeneous tree.

Yang and Ye [6] have studied strong theorems for countable nonhomogeneous Markov chains indexed by a homogeneous tree and the strong law of large numbers and the AEP for finite nonhomogeneous Markov chains indexed by a homogeneous tree.

Yang and Ye [9] studied strong theorems for countable nonhomogeneous Markov chains indexed by a homogeneous tree and the strong law of large numbers and the AEP for finite nonhomogeneous Markov chains indexed by a homogeneous tree.

Recently, Yang [4] has studied some strong limit theorems for countable homogeneous Markov chains indexed by a homogeneous tree and the strong law of large numbers and the asymptotic equipartition property (AEP) for finite homogeneous Markov chains indexed by a homogeneous tree.

I would have to build a chain of inference that led from the undoubted, countable presence of the "b's" and "p's" in the passage to Milton's intention and back again.

The term Markov chain is used to mean a Markov process which has a discrete (finite or countable) state-space.

Specifically, the class of countable-state, discrete-time Markov chains driven by additive Poisson noise, or lattice discrete-time Markov chains.