Quantum-logics-valued measure convergence theorem

In this paper, the following quantum-logic valued measure convergence theorem is proved: Let (L-1, 0, 1) be a Boolean algebra, (L-2, perpendicular to, circle plus, 0, 1) be a quantum logic and {mu(n) : n is an element of N} be a sequence of s-bounded (L-2, perpendicular to, circle plus, 0, 1)-valued measures which are defined on (L-1, 0, 1). If for each a is an element of (L-1, 0, 1), {mu(n)(a)}(n is an element of) (N) is an order topology tau(0)(L2) Cauchy sequence, when {nu(a)} convergent to 0, {mu(n)(a)} is order topology tau(0)(L2) convergent to 0 for each n is an element of N, where nu is a nonnegative finite additive measure which is defined on (L-1, 0,1), then when {nu(a)} convergent to 0, {mu(n)(a)} are order topology tau(0)(L2) convergent to 0 uniformly with respect to n is an element of N.