Result as to uniformly integrable sequence
Result as to uniformly integrable sequenceResult as to Uniformly Integrable SequenceResult Suppose that there exists r >1 and M < 1 such that EjXtXt kjr < M for all t , k andthatP 1j = 1 jhj j < 1 . Define Yt =P 1j = 1 hj Xt j . Then fYtYt kg is uniformaly integrable forany integer k. This implies that a product of uniformly integrable sequence is also uniformlyintegrable.ProofFirstly the productYtYt k takes the form ofYtYt k =1Xi= 1hiXt i1Xj = 1hj Xt k j =1Xi= 11Xj = 1hihj Xt iXt k jAccording to the definition of..出処::レポートサイトHAPPYCAMPUS!by HappyPartner