Article ID: CBB001552093

Vito Volterra's Construction of a Nonconstant Function with a Bounded, Non-Riemann Integrable Derivative (2015)

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In the 1880s the research on the theory of integration was focused mainly on the properties of infinite sets. The development of nowhere dense sets with positive outer content, known nowadays as nowhere dense sets with positive measure, allowed the construction of general functions with the purpose of extending Riemann's definition of integral. Vito Volterra provided, in 1881, an example of a differentiable function whose derivative is bounded but not Riemann integrable. In this article we present and discuss Volterra's example.

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https://data.isiscb.org/isis/citation/CBB001552093/

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Authors & Contributors
Sørensen, Henrik Kragh
Maligranda, Lech
Terepeta, Małgorzata
Jóźwik, Izabela
Oswald, Nicola M. R.
Wang, Quanlai
Concepts
Mathematics
Functions (mathematics)
Biographies
Mathematicians
Group theory
Sequences and series (mathematics)
Time Periods
19th century
20th century, early
20th century
18th century
Places
England
Scotland
Poland
Italy
Germany
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