A New Extension of the Riemann Integral

作者:Dawson C Bryan*
来源:AMERICAN MATHEMATICAL MONTHLY, 2018, 125(2): 130-140.
DOI:10.1080/00029890.2018.1401832

摘要

Using an equivalence relation on the hyperreals called approximation, a new extension of the Riemann integral is motivated and introduced in which every bounded function is integrable and for which there exists a function g : [0, 1] -> R simultaneously satisfying (1) g is integrable, (2) g is unbounded on every subinterval of [0, 1], and (3) g is identical to its average value function.

  • 出版日期2018