Positive definite forms generated by integrals and weak limits (Q794237)

The authors prove the following interesting theorem: If \(M_ k\geq \epsilon I\) for \(\epsilon>0\), and if the sequence \(\| H_ k(t)\|^ 2\) is uniformly integrable over [0,1], then there exists a sequence \(D_ k(t)\) of measurable \(m\times m\) sign-changing matrix-valued functions such that a subsequence of \(H_ k(t)D_ k(t)\) converges weakly in \(L_ 2\) to, say, \(B_ 0(t)\) and \(\int^{1}_{0}B_ 0(t)B_ 0(t)'dt\) is positive definite.