Functional analysis | Integrals

Pettis integral

In mathematics, the Pettis integral or Gelfand–Pettis integral, named after Israel M. Gelfand and Billy James 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. (Wikipedia).

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From playlist The Integral

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From playlist The Integral

Related pages

Borel set | Semi-reflexive space | Bochner integral | Lebesgue measure | Weak topology | Israel Gelfand | Mathematics | Measure space | Dual system | Convex hull | Quasi-complete space | Mean value theorem | Borel measure | Topological vector space