{"product_id":"stability-theorems-in-geometry-and-analysis-von-yu-g-reshetnyak","title":"Stability Theorems in Geometry and Analysis","description":"\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\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9780792331186\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9789048144679\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Hardcover - 9780792331186","offer_id":51238021062,"sku":"9780792331186","price":160.49,"currency_code":"EUR","in_stock":true},{"title":"Softcover - 9789048144679","offer_id":39415677288541,"sku":"9789048144679","price":160.49,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/83fdec9f-53fa-4637-857c-9c0ff5c56a23.jpg?v=1772262644","url":"https:\/\/shop.autorenwelt.de\/en\/products\/stability-theorems-in-geometry-and-analysis-von-yu-g-reshetnyak","provider":"Autorenwelt Shop","version":"1.0","type":"link"}