 I.e.for every fixed "t" in "E",

In almost all applications, one takes "E" = [0, "T"] or [0, +∞) and "M" = R"n" for some "n" in N. For brevity, write "C" for "C"([0, "T"]; R"n"); this is a vector space.Write "C"0 for the linear subspace consisting only of those functions that take the value zero at the infimum of the set "E".