Real Analysis Exchange

A Nice Example of Lebesgue Integration

Joseph L. Gerver

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We explore the properties of an interesting new example of a function which is Lebesgue integrable but not Riemann integrable.

Article information

Real Anal. Exchange, Volume 41, Number 2 (2016), 389-402.

First available in Project Euclid: 30 March 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26A42: Integrals of Riemann, Stieltjes and Lebesgue type [See also 28-XX]
Secondary: 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) {For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27}

Lebesgue integral upper semicontinuous numerical integration


Gerver, Joseph L. A Nice Example of Lebesgue Integration. Real Anal. Exchange 41 (2016), no. 2, 389--402.

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