In 1902 Henri Lebesgue (1875-1941) published his thesis containing a new theory of integration which was based on Borel's theory of measure. Independently of this William Henry Young (1863-1942) together with his wife Grace Chisholm Young (1868-1944) developed a similar theory of measure and integration. Only after submitting their papers on this subject to the London Mathematical Society did they learn about Lebesgue's results. Consequently the Youngs decided to publish a revised version in which the concept of Lebesgue was taken (...) into consideration and discussed. This parallel discovery will be analysed both from a mathematical and a psychological point of view. The previously unpublished primary sources from the private correspondence of the Youngs will be used to illuminate the collaboration between the Youngs and their reaction to Lebesgue. (shrink)