[I] feel a great debt of gratitude toward him.

He was invited to make a presentation to the seventh Congress of Scandinavian Mathematicians, held in Oslo from 19 to 22 August 1929. Jessen presented his theory of integration in German and in a particularly clear way, a very nice exposition with a reproduction of Hilbert's space-filling curve as it appeared in the original article of 1891, which shows at first glance that measure is preserved, the curve preserving throughout construction a perfect symmetry between the two axes. Jessen did not state his two theorems which he undoubtedly considered marginal, but announced a Fourier theory for functions with a countable infinity of periods. The transactions of the congress were published in 1930, so that at the proof stage Jessen could add a reference to Daniell of whom he had been informed meanwhile.

In Princeton Jessen met Aurel Wintner. Two more different mathematicians can hardly be imagined. Jessen was elegant, reserved, rigorous, scrupulous, Wintner was impassioned, a compulsive eater, overflowing with projects and works in progress, all done with great noise. Wintner was always interested in celestial mechanics and accordingly in almost periodic functions. For some time he had been studying the limiting laws of series of independent random variables of the type considered by Steinhaus, Jessen and others, what was called at the time the problem of infinite convolutions, on the line or in a finite-dimensional space. Wintner had obtained interesting results on the subject, which was one that Jessen had also come near to either alone or with Harald Bohr. Sometime in 1934, probably in the spring, Jessen and Wintner decided to pool their experience and write an article "Distribution functions and the Riemann zeta function" ...

Børge and Ellen had a son, Lars in 1934, but tragically the boy became ill of meningitis at the age of two and was disabled.

... probably because the other potential Danish applicants knew that they could not compete with him.

In 1960 the curriculum in mathematics was changed, and Jessen taught the second year analysis course. It comprised the basic knowledge about Fourier series, Lebesgue integration and complex analysis, but Jessen also liked to include basic results like Weierstrass' approximation theorem, Peano's curve and Weierstrass' nowhere differentiable continuous function. The lectures were very well prepared, and the blackboard was used in an efficient way, from the upper left corner to the lower right corner. Complicated drawings were often made beforehand and hidden behind another blackboard, and already written formulas were modified with coloured chalk to save writing. It was an aesthetic experience to attend Jessen's lectures. The essential points were made clear, and after the lecture one had the impression that everything was easy and elegant. Jessen enjoyed including small anecdotes about the mathematicians behind a theorem, and he often circulated books from the library during the lectures, so we could look at a portrait of a famous mathematician or at a classical mathematical paper. When lecturing about Jensen's inequality in convexity, he said jokingly that there were two mathematicians with the name of Jensen - the famous telephone engineer behind the formula, and himself when his name was misspelled. About Wintner he told us that his name was used for a physical unit: "One Wintner meant 100 cigarettes a day". Due to the increased number of students in the 1960s a new system involving teaching assistants was introduced with success. Two teaching assistants per class were chosen among the second year students and appointed as "fellow instructors". They had to learn the material at the same time as they helped their fellow students. On Saturday morning Jessen met with the fellow instructors and prepared them for the material to be covered in the lectures and exercises for the following week. I had the privilege of being such a fellow instructor and learned a lot because Jessen could not refrain from telling us many extra things. He also told us that he used to throw away the solutions of the exercises when the year was over, so that he had to rediscover the solutions every year. In this way, he was reminded about the difficulties of the exercises. At the final exam Jessen was always very favourable towards the students. He liked to cite Harald Bohr for having said that one should always give students a final grade that is a little higher than what they could expect. In that way they would always remember their years of study with joy. In addition to his teaching for the first or second year students, Jessen also gave courses for the students preparing for the Master's Degree. The lectures I followed were supported by handwritten notes of high quality distributed to the students. He liked to take up classical subjects such as conformal mapping, the Gamma function and the prime number theorem, where he could set a goal of obtaining a key result at the end.