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)
Read more about this topic: Egorov's Theorem
Famous quotes containing the words historical and/or note:
“Culture is the name for what people are interested in, their thoughts, their models, the books they read and the speeches they hear, their table-talk, gossip, controversies, historical sense and scientific training, the values they appreciate, the quality of life they admire. All communities have a culture. It is the climate of their civilization.”
—Walter Lippmann (18891974)
“During the cattle drives, Texas cowboy music came into national significance. Its practical purpose is well knownit was used primarily to keep the herds quiet at night, for often a ballad sung loudly and continuously enough might prevent a stampede. However, the cowboy also sang because he liked to sing.... In this music of the range and trail is the grayness of the prairies, the mournful minor note of a Texas norther, and a rhythm that fits the gait of the cowboys pony.”
—Administration in the State of Texa, U.S. public relief program (1935-1943)