Statement
Suppose U is an open set in the Euclidean space Rn, and suppose that f0, f1 ... is a sequence of smooth, complex-valued functions on U. If I is an any open interval in R containing 0 (possibly I = R), then there exists a complex-valued smooth function F(t, x) defined on I×U, such that
for k ≥ 0 and x in U.
Read more about this topic: Borel's Lemma
Famous quotes containing the word statement:
“He has the common feeling of his profession. He enjoys a statement twice as much if it appears in fine print, and anything that turns up in a footnote ... takes on the character of divine revelation.”
—Margaret Halsey (b. 1910)
“Children should know there are limits to family finances or they will confuse “we can’t afford that” with “they don’t want me to have it.” The first statement is a realistic and objective assessment of a situation, while the other carries an emotional message.”
—Jean Ross Peterson (20th century)
“The force of truth that a statement imparts, then, its prominence among the hordes of recorded observations that I may optionally apply to my own life, depends, in addition to the sense that it is argumentatively defensible, on the sense that someone like me, and someone I like, whose voice is audible and who is at least notionally in the same room with me, does or can possibly hold it to be compellingly true.”
—Nicholson Baker (b. 1957)