Stability Theorems in Geometry and Analysis - Yu. G. Reshetnyak
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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 Gi ... Full description
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Description
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.
More Information
| Author | Yu. G. Reshetnyak |
|---|---|
| Publisher | Springer Netherlands |
| Series | Mathematics and Its Applications |
| Release year | 1994 |
| Cover type | Hardcover |
| EAN | 9780792331186 |