| Summary: | We analyze the notion of reproducing pairs of weakly measurable functions, a generalization of continuous frames. The aim is to represent elements of an abstract space <i>Y</i> as superpositions of weakly measurable functions belonging to a space <inline-formula> <math display="inline"> <semantics> <mrow> <mi>Z</mi> <mo>:</mo> <mo>=</mo> <mi>Z</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo>,</mo> <mi>μ</mi> <mo stretchy="false">)</mo></mrow></semantics></math></inline-formula>, where <inline-formula> <math display="inline"> <semantics> <mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo>,</mo> <mi>μ</mi> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula> is a measure space. Three cases are envisaged, with increasing generality: (i) <i>Y</i> and <i>Z</i> are both Hilbert spaces; (ii) <i>Y</i> is a Hilbert space, but <i>Z</i> is a <span style="font-variant: small-caps;">pip</span>-space; (iii) <i>Y</i> and <i>Z</i> are both <span style="font-variant: small-caps;">pip</span>-spaces. It is shown, in particular, that the requirement that a pair of measurable functions be reproducing strongly constrains the structure of the initial space <i>Y</i>. Examples are presented for each case.
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