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In order to study inclusions of the type Lp(μ,X)⊂Lq(ν,Y), we introduce the notion of anL-correspondence. After proving some basic theorems, we give characterizations of some types of L-correspondencesand offer a conjecture that is similar to an equimeasurability theorem

international journal of mathematics and mathematical sciences

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$L$" id="E1"><mml:mi>L</mml:mi></mml:math>-correspondences: the inclusion<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$L^p(\mu,X) \subset L^q(\nu,Y)$" id="E2"><mml:msup><mml:mi>L</mml:mi><mml:mi>p</mml:mi></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>μ</mml:mi><mml:mo>,</mml:mo><mml:mi>X</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>⊂</mml:mo><mml:msup><mml:mi>L</mml:mi><mml:mi>q</mml:mi…

L-correspondences: the inclusionLp(μ,X)⊂Lq