测度无限集上叶果落夫定理成立的充分必要条件及应用

Sufficient And Necessary Condition That Eг ОРОВ 'S Theorem is Accurate on Measure Infinite Set

获得了测度无限集上叶果落夫定理成立的充分必要条件,即证明了fn(x)n→+∞a..ef(x)于E,且1k,■N,m∞∪n=NE[|fn-f|≥1k]<+∞对δ>0,■可测集FδE,m(E-Fδ)<δ,满足fn(x)n→∞一致f(x)于Fδ,并给出了此结果的应用.

Sufficient and necessary condition that ErOPOB Theorem is accurate is obtained on Measure Infinite Set. Namely, that fn（x） n→＋∞ → a、、ef （x） almost everywhere convergence on E, and A 1/k, N,m U N=n ∞ E[lfn-fl≥1/k]〈＋∞ 对 δ〉0, Fδ E,m（E-Fδ）〈δ satisfy fn（x） n→f（x） uniform convergence on Fδ is proved. The applications of this resuh are given.