Alexandru Froda

Froda's major contribution was in the field of mathematical analysis. His first important result^[3] was concerned with the set of discontinuities of a real-valued function of a real variable. In this theorem Froda proves that the set of simple discontinuities of a real-valued function of a real variable is at most countable.

In a paper^[4] from 1936 he proved a necessary and sufficient condition for a function to be measurable. In the theory of algebraic equations, Froda proved^[5] a method of solving algebraic equations having complex coefficients.

In 1929 Dimitrie Pompeiu conjectured that any continuous function of two real variables defined on the entire plane is constant if the integral over any circle in the plane is constant. In the same year^[6] Froda proved that, in the case that the conjecture is true, the condition that the function is defined on the whole plane is indispensable. Later it was shown that the conjecture is not true in general.

In 1907 Pompeiu constructed an example of a continuous function with a nonzero derivative which has a zero in every interval. Using this result Froda finds a new way of looking at an older problem^[7] posed by Mikhail Lavrentyev in 1925, namely whether there is a function of two real variables such that the ordinary differential equation ${\displaystyle dy=f(x,y)dx}$ has at least two solutions passing through every point in the plane.

In the theory of numbers, beside rational triangles^[8] he also proved several conditions^{[9][10][11][12][13]} for a real number, which is the limit of a rational convergent sequence, to be irrational, extending a previous result of Viggo Brun from 1910.^[14]

In 1937 Froda independently noticed and proved the case ${\displaystyle n=1}$ of the Borsuk–Ulam theorem. He died in Bucharest in 1973.

• Froda's theorem