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- W4233014681 abstract "This chapter motivates the Riemann sum approach to random variation and indicates how it relates to the traditional Lebesgue or Kolmogorov approach. The Riemann-complete and Stieltjes-complete integrals are extensions of the corresponding Lebesgue integrals. The chapter compares the calculus or Newton integral with the Riemann-complete integral. It demonstrates the Riemann-complete integrability of some functions, using the positive functions δ. The chapter indicates how the Riemann sum approach ties in naturally and intuitively with the Stieltjes-complete theory of integration using δ-gauges. It highlights some features and methods of the δ-gauges theory of integration which are specific to that theory and which are less evident in other integration theories. This is done with a view to preparing the way for more formal presentation of a Riemann sum approach to the analysis of random variability using the Henstock integral itself. The chapter also discusses the Cauchy extension of the Riemann Integral. Controlled Vocabulary Terms calculus integral; Cauchy integral; Lebesgue integral; random variable; Riemann integral" @default.
- W4233014681 created "2022-05-12" @default.
- W4233014681 date "2012-10-08" @default.
- W4233014681 modified "2023-10-17" @default.
- W4233014681 title "Introduction" @default.
- W4233014681 doi "https://doi.org/10.1002/9781118345955.ch2" @default.
- W4233014681 hasPublicationYear "2012" @default.
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