9780792331186 - Stability Theorems in Geometry and Analysis (Mathematics and Its Applications, 304, Band 304) von Reshetnyak, Yu.G. (2 Ergebnisse)

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Buch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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~, (x, y) = XIYl + X2Y2 + . + XnYn. n Given arbitrary points a and b in lR. , we denote by [a, b] the segment that joins n them, i.e. the collection of points x E lR. of the form 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.