Results 11 to 20 of about 51,902 (192)
Representation of maxitive measures: an overview [PDF]
, 2015 Idempotent integration is an analogue of Lebesgue integration where $\sigma$-maxitive measures replace $\sigma$-additive measures. In addition to reviewing and unifying several Radon--Nikodym like theorems proven in the literature for the idempotent ...
Poncet, Paul
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On extending the Lebesgue integral [PDF]
Proceedings of the American Mathematical Society, 1981 In this paper continuous extensions of the Lebesgue Integral which integrate their almost everywhere approximate derivatives are considered. First, those extensions which are generated by a single function are characterized. Then the largest extension which is contained in all maximal extensions is considered and shown to contain the wide sense Denjoy ...
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New criteria to identify spectrum [PDF]
, 2003 In this paper we give some new criteria for identifying the components of a probability measure, in its Lebesgue decomposition. This enables us to give new criteria to identify spectral types of self-adjoint operators on Hilbert spaces, especially those ...
Jensen, A, Krishna, M
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Fractional integrals and derivatives: mapping properties [PDF]
, 2016 This survey is aimed at the audience of readers interested in the information on mapping properties of various forms of fractional integration operators, including multidimensional ones, in a large scale of various known function spaces.As is well known,
Rafeiro, Humberto, Samko, Stefan
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A Characterization of the Lebesgue Integral [PDF]
Canadian Mathematical Bulletin, 1977 The first general integrability criterion is due to Riemann. He observed that a necessary and sufficient condition for a function f(x) on [a, b] to be integrable in his sense is that for each ε > 0 there exists a δ > 0 so thatwhere {x0, x1, …, xn} is a partition of [a, b] with diameter less than δ (and ω(f, I) denotes the oscillation of f on the ...
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Kurzweil’s PU integral as the Lebesgue integral [PDF]
Mathematica Bohemica, 2006 Summary: For a merely continuous partition of unity the PU integral is the Lebesgue integral.
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An elementary way to introduce a Perron-like integral [PDF]
, 2010 We give an alternative definition of integral at the generality of the Perron integral and propose an exposition of the foundations of integral theory starting from this new definition.
Bendová, Hana, Malý, Jan
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The idempotent Radon--Nikodym theorem has a converse statement
, 2013 Idempotent integration is an analogue of the Lebesgue integration where $\sigma$-additive measures are replaced by $\sigma$-maxitive measures. It has proved useful in many areas of mathematics such as fuzzy set theory, optimization, idempotent analysis ...
Poncet, Paul
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The Gauge Integral Theory in HOL4
Journal of Applied Mathematics, 2013 The integral is one of the most important foundations for modeling dynamical systems. The gauge integral is a generalization of the Riemann integral and the Lebesgue integral and applies to a much wider class of functions. In this paper, we formalize the
Zhiping Shi +6 more
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Rectified fractional order iterative learning control for linear system with initial state shift
Advances in Difference Equations, 2018 In this paper, a new rectifying action is combined into different proportional-α-order-derivative-type iterative learning control algorithms for a class of fractional order linear time-invariant systems.
Lei Li
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