1. Preliminaries, Notation, and Terminology n n 1.1. Sets and functions in lR. • Throughout the book, lR. stands for the n-dimensional arithmetic space of points x = (X},X2,'" ,xn)j Ixl is the length of n n a vector x E lR. and (x, y) is the scalar product of vectors x and y in lR. , i. e., for x = (Xl, X2, •.• , xn) and y = (y}, Y2,-., Yn), Ixl = Jx< + x< + ... + x. a + I'b, where>. + I' = 1 and >. < 0, I' < O. n We denote by ei, i = 1, 2, ... ,n, the vector in lR. whose ith coordinate is equal to 1 and the others vanish. The vectors el, e2, ... ,en form a basis for the space n lR. , which is called canonical. If P( x) is some proposition in a variable x and A is a set, then {x E A I P(x)} denotes the collection of all the elements of A for which the proposition P( x) is true. | Stability Theorems in Geometry and Analysis by Yu. G. Reshetnyak, Paperback | Indigo Chapters | Stability Theorems in Geometry and Analysis by Yu.G. Reshetnyak, Paperback | Indigo Chapters