# Mathematician:Bernard Osgood Koopman

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## Mathematician

French-born American mathematician, known for his work in ergodic theory, the foundations of probability, statistical theory and operations research.

## Nationality

French-born American

## History

- Born: 19 January 1900 in 7th arrondissement of Paris, France
- Died: 18 August 1981 in Randolph, New Hampshire, US

## Theorems and Definitions

- Pitman-Koopman-Darmois Theorem (with Edwin James George Pitman and Georges Darmois) (also known as the Koopman-Pitman-Darmois Theorem or Pitman-Koopman Theorem)

- Koopman-von Neumann Classical Mechanics (with John von Neumann)
- Koopman Operator
- Koopman-Darmois Family of Distributions (also known as the Exponential Family of Distributions) (with Georges Darmois)

Results named for **Bernard Osgood Koopman** can be found here.

Definitions of concepts named for **Bernard Osgood Koopman** can be found here.

## Publications

- 1931:
*Hamiltonian Systems and Transformations in Hilbert Space*(*Proc. Natl. Acad. Sci. U S A***Vol. 17**,*no. 5*: pp. 315 – 318) - 1936:
*On distributions admitting a sufficient statistic*(*Trans. Amer. Math. Soc.***Vol. 39**,*no. 3*: pp. 399 – 409) (in which Pitman-Koopman-Darmois Theorem is presented) - 1940:
*The axioms and algebra of intuitive probability*(*Ann. Math.***Vol. 41**: pp. 269 – 292) - 1940:
*The bases of probability*(*Bull. Amer. Math. Soc.***Vol. 46**: pp. 763 – 774) - 1941:
*Intuitive probabilities and sequences*(*Ann. Math.***Vol. 42**: pp. 169 – 187)

- 1946:
*Search and Screening*