## American Mathematical Society TranslationsTranslations of articles on mathematics appearing in various Russian mathematical serials. |

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### Contents

E On limits of indeterminacy of partial sums of universal | 1 |

E On limit functions of trigonometric series MeHbillOB | 35 |

E Universal sequences of functions MeHbillOB L E 06 | 65 |

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arbitrary assume basis block matrix consider converges in measure corresponding countable set defined a.e. defined almost everywhere Definition denote equal equations equiconvergent almost everywhere fk(x Fl(x fm(x fmk(x func function of 2.3 functions p(x gm(x Hankel Hankel operators Hence Hilbert space hm(x holds a.e. hypothesis increasing sequence inequality Lemma lim meas limit function limit superior limits in measure linear extension lower limits Lp(T matrix matrix-valued function measurable and defined measurable function f(x measurable set Moreover natural numbers mk objective function obtain optimal control p)-extensions p)-functions partial sums positive measure positive number problem proof of Theorem properties proved quasi-ball satisfies condition satisfy the conditions segment sense of convergence sequence 2.3 sequence of functions sequence of natural sequence of type series of type singular integral operator solution suppose taking on values tion type A(FV F2 upper and lower upper limit vector