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Reference.org
Pettis integral
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the Pettis integral or Gelfand–Pettis integral, named after <a href="/facts/Israel_Gelfand/TJeJouKs">Israel M. Gelfand</a> and <a href="/facts/Billy_James_Pettis/pG9mrUKr">Billy James Pettis</a>, extends the definition of the <a href="/facts/Lebesgue_integral/f4AgvC6x">Lebesgue integral</a> to vector-valued functions on a <a href="/facts/Measure_space/w9Dx4KY1">measure space</a>, by exploiting <a href="/facts/Dual_system/2Y8KyofV">duality</a>. The integral was introduced by Gelfand for the case when the measure space is an interval with <a href="/facts/Lebesgue_measure/8us9cGoW">Lebesgue measure</a>. The integral is also called the weak integral in contrast to the <a href="/facts/Bochner_integral/RpzcTu9n">Bochner integral</a>, which is the strong integral. </p>