{ "item_title" : "Stability Theorems in Geometry and Analysis", "item_author" : [" Yu G. Reshetnyak "], "item_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 bya, 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.", "item_img_path" : "https://covers4.booksamillion.com/covers/bam/9/04/814/467/9048144671_b.jpg", "price_data" : { "retail_price" : "169.99", "online_price" : "169.99", "our_price" : "169.99", "club_price" : "169.99", "savings_pct" : "0", "savings_amt" : "0.00", "club_savings_pct" : "0", "club_savings_amt" : "0.00", "discount_pct" : "10", "store_price" : "" } }

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