Pettis integral

（重定向自Weak integral）

In mathematics, the Pettis integral or Gelfand–Pettis integral, named after I. M. Gelfand and B. J. Pettis, extends the definition of the Lebesgue integral to vector-valued functions on a measure space, by exploiting duality. The integral was introduced by Gelfand for the case when the measure space is an interval with Lebesgue measure. The integral is also called the weak integral in contrast to the Bochner integral, which is the strong integral.

单词	Weak integral
释义	Weak integral 英语百科 Pettis integral （重定向自Weak integral） In mathematics, the Pettis integral or Gelfand–Pettis integral, named after I. M. Gelfand and B. J. Pettis, extends the definition of the Lebesgue integral to vector-valued functions on a measure space, by exploiting duality. The integral was introduced by Gelfand for the case when the measure space is an interval with Lebesgue measure. The integral is also called the weak integral in contrast to the Bochner integral, which is the strong integral.
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