In mathematics, particularly functional analysis, the Dunford–Schwartz theorem, named after Nelson Dunford and Jacob T. Schwartz states that the averages of powers of certain norm-bounded operators on L1 converge in a suitable sense.Theorem. Let be a linear operator from to with and . Then exists almost everywhere for all .The statement is no longer true when the boundedness condition is relaxed to even .

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  • In mathematics, particularly functional analysis, the Dunford–Schwartz theorem, named after Nelson Dunford and Jacob T. Schwartz states that the averages of powers of certain norm-bounded operators on L1 converge in a suitable sense.Theorem. Let be a linear operator from to with and . Then exists almost everywhere for all .The statement is no longer true when the boundedness condition is relaxed to even .
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  • In mathematics, particularly functional analysis, the Dunford–Schwartz theorem, named after Nelson Dunford and Jacob T. Schwartz states that the averages of powers of certain norm-bounded operators on L1 converge in a suitable sense.Theorem. Let be a linear operator from to with and . Then exists almost everywhere for all .The statement is no longer true when the boundedness condition is relaxed to even .
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  • Théorème de Dunford-Schwartz
  • Dunford–Schwartz theorem
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