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- W4220890072 abstract "Abstract We present a new approach to define a suitable integral for functions with values in quasi-Banach spaces. The integrals of Bochner and Riemann have deficiencies in the non-locally convex setting. The study of an integral for p -Banach spaces initiated by Vogt is neither totally satisfactory, since there are quasi-Banach spaces which are p -convex for all $$0<p<1$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo><</mml:mo> <mml:mi>p</mml:mi> <mml:mo><</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> , so it is not always possible to choose an optimal p to develop the integration. Our method puts the emphasis on the galb of the space, which permits a precise definition of its convexity. The integration works for all spaces of galbs known in the literature. We finish with a fundamental theorem of calculus for our integral." @default.
- W4220890072 created "2022-04-03" @default.
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- W4220890072 date "2022-03-20" @default.
- W4220890072 modified "2023-09-30" @default.
- W4220890072 title "Toward an optimal theory of integration for functions taking values in quasi-Banach spaces" @default.
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- W4220890072 doi "https://doi.org/10.1007/s13398-022-01230-8" @default.
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