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

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 <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="section-sign section-sign 5"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="normal"> § </mml:mi> <mml:mi mathvariant="normal"> § </mml:mi> <mml:mn>5</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">\S \S 5</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="6"> <mml:semantics> <mml:mn>6</mml:mn> <mml:annotation encoding="application/x-tex">6</mml:annotation> </mml:semantics> </mml:math> </inline-formula> .

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