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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The weighted pointwise ergodic theorem and the individual ergodic theorem along subsequences

Authors: A. Bellow and V. Losert
Journal: Trans. Amer. Math. Soc. 288 (1985), 307-345
MSC: Primary 28D05
MathSciNet review: 773063
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Abstract: In this paper on the weighted pointwise ergodic theorem we bring together a substantial amount of previous work by a number of mathematicians and integrate it into a systematic consistent scheme; we also bring some original contributions to the subject which extend its boundaries and suggest further avenues of research. The paper is divided into six sections. The most significant new results are contained in $\S \S 5$ and $6$.

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Keywords: Automorphism, ergodic, discrete spectrum, countable Lebesgue spectrum, <IMG WIDTH="24" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$K$">-automorphism, "good universal weight", positive definite function, affinity of two probability measures (=Hellinger integral), correlation of a sequence, spectral measure corresponding to a sequence, Besicovitch class <IMG WIDTH="48" HEIGHT="41" ALIGN="MIDDLE" BORDER="0" SRC="images/img2.gif" ALT="$B(p)$">, almost periodic functions (in the sense of Bohr, Weyl, Eberlein), Bochner-Fej&#233;r polynomial, strictly <IMG WIDTH="19" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img8.gif" ALT="$L$">-stable dynamical system, "uniform sequence", Bohr compactification, sequence that satisfies a "uniform order conditin on <IMG WIDTH="19" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img7.gif" ALT="$J$">", "saturating sequence", Weak Maximal Inequality, "bad universal sequence", "block sequence", lacunary sequence, "good universal sequence" of density zero
Article copyright: © Copyright 1985 American Mathematical Society