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:
“If we do take statements to be the primary bearers of truth, there seems to be a very simple answer to the question, what is it for them to be true: for a statement to be true is for things to be as they are stated to be.”
—J.L. (John Langshaw)
“No statement about God is simply, literally true. God is far more than can be measured, described, defined in ordinary language, or pinned down to any particular happening.”
—David Jenkins (b. 1925)
“A sentence is made up of words, a statement is made in words.... Statements are made, words or sentences are used.”
—J.L. (John Langshaw)