Egorov's Theorem - Historical Note

Historical Note

The first proof of the theorem was given by Carlo Severini in 1910 and was published in (Severini 1910): he used the result as a tool in his research on series of orthogonal functions. His work remained apparently unnoticed outside Italy, probably due to the fact that it is written in Italian, appeared in a scientific journal with limited diffusion and was considered only as a means to obtain other theorems. A year later Dmitri Egorov published his independently proved results in the note (Egoroff 1911), and the theorem become widely known under his name: however it is not uncommon to find references to this theorem as the Severini–Egoroff theorem or Severini–Egorov Theorem. According to Cafiero (1959, p. 315) and Saks (1937, p. 17), the first mathematicians to prove independently the theorem in the nowadays common abstract measure space setting were Frigyes Riesz in (Riesz 1922), (Riesz 1928), and Wacław Sierpiński in (Sierpiński 1928): an earlier generalization is due to Nikolai Luzin, who succeeded in slightly relaxing the requirement of finiteness of measure of the domain of convergence of the pointwise converging functions in the ample paper (Luzin 1916), as Saks (1937, p. 19) recalls. Further generalizations were given much later by Pavel Korovkin, in the paper (Korovkin 1947), and by Gabriel Mokobodzki in the paper (Mokobodzki 1970)