Stability Theorems in Geometry and Analysis (Hardcover, 1994 ed.)

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.

General

Imprint:	Springer
Country of origin:	Netherlands
Series:	Mathematics and Its Applications, 304
Release date:	September 1994
First published:	September 1994
Authors:	Yu. G. Reshetnyak
Dimensions:	234 x 156 x 23mm (L x W x T)
Format:	Hardcover
Pages:	394
Edition:	1994 ed.
ISBN-13:	978-0-7923-3118-6
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Integral equations
LSN:	0-7923-3118-4
Barcode:	9780792331186

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