Search results for "Locally integrable function"

showing 2 items of 12 documents

On the Minimal Solution of the Problem of Primitives

2000

Abstract We characterize the primitives of the minimal extension of the Lebesgue integral which also integrates the derivatives of differentiable functions (called the C -integral). Then we prove that each BV function is a multiplier for the C -integral and that the product of a derivative and a BV function is a derivative modulo a Lebesgue integrable function having arbitrarily small L 1 -norm.

Pure mathematicsApplied MathematicsModuloMathematical analysisRiemann integralLebesgue integrationWeak derivativeMultiplier (Fourier analysis)symbols.namesakeBounded variationsymbolsLocally integrable functionDifferentiable functionAnalysisMathematicsJournal of Mathematical Analysis and Applications
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APPROXIMATION OF BANACH SPACE VALUED NON-ABSOLUTELY INTEGRABLE FUNCTIONS BY STEP FUNCTIONS

2008

AbstractThe approximation of Banach space valued non-absolutely integrable functions by step functions is studied. It is proved that a Henstock integrable function can be approximated by a sequence of step functions in the Alexiewicz norm, while a Henstock–Kurzweil–Pettis and a Denjoy–Khintchine–Pettis integrable function can be only scalarly approximated in the Alexiewicz norm by a sequence of step functions. In case of Henstock–Kurzweil–Pettis and Denjoy–Khintchine–Pettis integrals the full approximation can be done if and only if the range of the integral is norm relatively compact.

Sobolev spacePure mathematicsRelatively compact subspaceIntegrable systemGeneral MathematicsNorm (mathematics)Step functionMathematical analysisBounded variationBanach spaceLocally integrable functionMathematicsGlasgow Mathematical Journal
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