Decomposition integral without alternatives, its equivalence to Lebesgue integral, and computational algorithms

In this paper we present a new class of decomposition integrals called the collection integrals. from this class of integrals we take a closer look on two special types of collection integrals, namely the chain integral and the minmax integral. Superdecomposition version of collection integral is also defined and the superdecomposition duals for the chain and the min-max integrals are presented. Also, the condition on the collection that ensures the coincidence of the collection integral with the Lebesgue integral is presented. Lastly, some computational algorithms are discussed.

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Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).