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Author McShane, E. J. (Edward James), 1904-1989.

Title A Riemann-type integral that includes Lebesgue-Stieltjes, Bochner and stochastic integrals / by E.J. McShane
Published Providence, R.I. : American Mathematical Society, 1969

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Description 1 online resource (54 pages)
Series Memoirs of the American Mathematical Society ; no. 88
Memoirs of the American Mathematical Society ; no. 88.
Contents Introduction -- Preliminaries concerning semi-groups and limits -- Notation and definitions -- Elementary properties -- Henstock's lemma -- Absolute integrability -- The monotone convergence theorem -- The dominated convergence theorem -- A more traditional type of integral -- Convergence theorems -- Measure -- Examples : integrals of Stieltjes type -- Examples -- The Bochner, Pettis and Bogdanowicz integrals -- Stochastic integrals
Summary One of the difficulties with integration theory is that there are so many different detailed definitions that the non-expert is confused about their relative strengths and usefulness. A surprising recent development in the theory of integration has been the discovery that suitable modifications to the Riemann definition using approximating sums can produce a wide variety of different integrals including integrals of great power
Bibliography Includes bibliographical references (pages 53-54)
Notes Print version record
Subject Integrals.
Lebesgue integral.
Integrals, Bochner.
Integrals, Generalized.
Pettis integral.
Stochastic integrals.
Stochastic integrals
Pettis integral
Lebesgue integral
Integrals, Generalized
Integrals, Bochner
Integrals
Bochner-Integral
Lebesgue-Stieltjes-Integral
Riemannsches Integral
Stochastisches Integral
Form Electronic book
ISBN 9781470400378
1470400375