{"product_id":"stability-theorems-in-geometry-and-analysis-9780792331186","title":"Stability Theorems in Geometry and Analysis","description":"\u003cp\u003e • Author(s): Yu G. Reshetnyak\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: Geometry - Differential\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e1. 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 = \u0026gt;.a + I'b, where\u0026gt;. + I' = 1 and \u0026gt;. 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.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Hardcover","offer_id":45284265623703,"sku":"9780792331186","price":10915.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9780792331186.webp?v=1769280666","url":"https:\/\/atlanticbooks.com\/products\/stability-theorems-in-geometry-and-analysis-9780792331186","provider":"Atlantic Books","version":"1.0","type":"link"}