1,720,969 research outputs found
A Volterra type derivative of the Lebesgue integral
No full textUsing functions of bounded variation, we define a Volterra type derivative of the linear functional associated with a Lebesgue integrable function and show that it is equal to this function almost everywhere.</p
A Riemann type definition of a variational integral
No full textWe present a Riemann type definition of a coordinate free integral for which a general divergence theorem holds. The definition is particularly simple in dimension one.</p
A note on the generalized Riemann integral
No full textWe show that the generalized Riemann integral can be defined by means of gage functions which are upper semicontinuous when restricted to a suitable subset whose complement has measure zero.</p
An invariant Riemann type integral defined by figures
No full textWe show that a multidimensional generalized Riemann integral defined by means of rectangular figures is already invariant with respect to lipeomorphic changes of coordinates.</p
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