Work
He was awarded the Cambridge B.A. in 1944 and began research for the PhD in London, which he gained in December 1948 with a thesis entitled Interval Functions and their Integrals, an extension of J. C. Burkill's theory. His Ph.D. examiners were Burkill and H. Kestelman. In 1947 he returned briefly to Cambridge to complete the undergraduate mathematical studies which had been truncated by his Ministry of Supply work.
Most of Henstock's work was concerned with integration. From initial studies of the Burkill and Ward integrals he formulated an integration process whereby the domain of integration is suitably partitioned for Riemann sums to approximate the integral of a function. His methods led to an integral on the real line that was very similar in construction and simplicity to the Riemann integral but which included the Lebesgue integral and, in addition, allowed non-absolute convergence.
These ideas were developed from the late 1950s. Independently, Jaroslav Kurzweil developed a similar Riemann-type integral on the real line. The resulting integral is now known as the Henstock-Kurzweil integral. On the real line it is equivalent to the Denjoy-Perron integral, but has a simpler definition.
In the following decades, Henstock developed extensively the distinctive features of his theory, inventing the concepts of division spaces or integration bases to demonstrate in general settings the properties and characteristics of mathematical integration. His theory provides a unified approach to non-absolute integral, as different kinds of Henstock integral, choosing an appropriate integration basis (division space, in Henstock's own terminology). It has been used in differential and integral equations, harmonic analysis, probability theory and Feynman integration. Numerous monographs and texts have appeared since 1980 and there have been several conferences devoted to the theory. It has been taught in standard courses in mathematical analysis.
Henstock was author of 46 journal papers in the period 1946 to 2006. He published four books on analysis (Theory of Integration, 1963; Linear Analysis, 1967; Lectures on the Theory of Integration, 1988; and The General Theory of Integration, 1991). He wrote 171 reviews for MathSciNet. In 1994 he was awarded the Andy Prize of the XVIII Summer Symposium in Real Analysis. His academic career began as Assistant Lecturer, Bedford College for Women, 1947–48; then Assistant Lecturer at Birkbeck, 1948–51; Lecturer, Queen's University Belfast, 1951–56; Lecturer, Bristol University, 1956–60; Senior Lecturer and Reader, Queen’s University Belfast, 1960–64; Reader, Lancaster University, 1964–70; Chair of Pure Mathematics, New University of Ulster, 1970–88; and Leverhulme Fellow 1988-91.
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