# Percy John Daniell

**Percy John Daniell** (9 January 1889 – 25 May 1946) was a pure and applied mathematician. In a series of papers published between 1918 and 1928, he developed and expanded a generalized theory of integration and differentiation, which is today known as the Daniell integral. In the setting of integration, he also worked on results that lead to the Daniell-Kolmogorov extension theorem in the theory of stochastic processes, independently of Andrey Kolmogorov.[1] He was an Invited Speaker of the ICM in 1920 at Strasbourg.[2]

Daniell was born in Valparaiso, Chile. His family returned to England in 1895. Daniell attended King Edward's School, Birmingham and proceeded to Trinity College, Cambridge (where he was the last Senior Wrangler in 1909). At this time Daniell was an applied mathematician/theoretical physicist. For a year he lectured at the University of Liverpool and then he was appointed to the new Rice Institute in Houston, Texas. The Rice Institute had him spend a year at the University of Göttingen studying with Max Born and David Hilbert. Daniell was at Rice from 1914 to 1923 when he returned to England to a chair at the University of Sheffield. During World War II Daniell advised the British Ministry of Supply. The strain of work during the war took a heavy toll on his health. He died on 25 May 1946, after having collapsed at his home a few weeks earlier.

## External links

Aldrich, J. (2007) "But you have to remember P.J.Daniell of Sheffield" Electronic Journ@l for History of Probability and Statistics December 2007.

## References

- J. Aldrich, But you have to remember PJ Daniell of Sheffield, Electronic Journal for History of Probability and Statistics, Vol. 3, number 2, 2007
- "
*Stieltjes-Volterra Products*by P. J. Daniell" (PDF).*Compte rendu du Congrès international des mathématiciens tenu à Strasbourg du 22 au 30 Septembre 1920*. 1921. pp. 130–136.

- Stewart, C.A. (1947), "P. J. Daniell",
*J. London Math. Soc.***s1**-22: 75–80. - Daniell, Percy John (1918), "A general form of integral",
*Annals of Mathematics***19**: 279–94. - –––––– (1919a), "Integrals in an infinite number of dimensions",
*Annals of Mathematics***20**: 281–88. - –––––– (1919b), "Functions of limited variation in an infinite number of dimensions",
*Annals of Mathematics***21**: 30–38. - –––––– (1920), "Further properties of the general integral",
*Annals of Mathematics***21**: 203–20. - –––––– (1921), "Integral products and probability",
*American Journal of Mathematics***43**: 143–62. - –––––– (1946), "Discussion on the Symposium on Autocorrelation in Time Series",
*Supplement to the Journal of the Royal Statistical Society***8**-1: 88–90. - Shilov, G. E., and Gurevich, B. L. (1978),
*Integral, Measure, and Derivative: A Unified Approach,*Richard A. Silverman, trans., Dover Publications. ISBN 0-486-63519-8