Let ({ G_{k}, k=1,2,ldots}) be at most countable collection of unbounded open subsets of ((0, infty)).
By the Vitali lemma (see [13]), there exists (Lambda_{j} subset E_{j} epsilon; mu, zeta)), which is at most countable, such that ((B P_{j,i},rho_{j,i}):P_{j,i}inLambda_{j} )) are disjoint and (E_{j} epsilon; mu, zeta) subset bigcup_{P_{j,i}inLambda_{j}} B P_{j,i},5rho_{j,i})).
By the Vitali lemma (see [15]), there exists (Lambda_{j} subset E_{j} epsilon; lambda, 1)), which is at most countable, such that ({B(P_{j,i},rho_{j,i}):P_{j,i}inLambda_{j} }) are disjoint and (E_{j} epsilon; lambda, 1) subset bigcup_{P_{j,i}inLambda_{j}} B(P_{j,i},5rho_{j,i})).
By the Vitali lemma (see [9]), there exists (Lambda_{k} subset E_{k} epsilon; lambda, beta)), which is at most countable, such that ({B(P_{k,i},rho_{k,i}):P_{k,i}inLambda_{k} }) are disjoint and (E_{k} epsilon; lambda, beta) subset bigcup_{P_{k,i}inLambda_{k}} B(P_{k,i}, 5rho_{k,i})).
In general, nothing need be assumed about this set; in what follows, I will assume that E is at most countable, that is, that there are at most countably many evidence items.
Finally, all the corresponding results for a Fock space with any, at most countable, multiplicity are given.
Therefore, is at most countable.
Σ ( A ) is at most countable.
Let, then is a countable subset and (2.3).
Choose any countable subset of and set Suppose that (3.40).
