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Work: Purely non-atomic weak $L^p$ spaces

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2. Lack of isomorphic embeddings of sequence space ℓ, into <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"> <mml:msub> <mml:mrow> <mml:mi>L</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>,</mml:mo> <mml:mi>q</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:mi mathvariant="script">M</mml:mi> <mml:mo>,</mml:mo> <mml:mi>τ</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> over a noncommutative probability space

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