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A mapping theorem for logarithmic and integration-by-parts operators

A mapping theorem for logarithmic and integration-by-parts operators

Suppose <italic>U</italic> is a set, <bold>F</bold> is a field of subsets of <italic>U</italic>, <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="German p Subscript upper A upper B"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="fraktur">p</mml:mi> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>A</mml:mi> <mml:mi>B</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">{\mathfrak {p}_{AB}}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is the set of …