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" The proof of this theorem is completely analogous to the proof of Theorem 8, Chapter VII, and need not be repeated here. "
Projective Geometry - Page 264
by Oswald Veblen, John Wesley Young - 1910
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Projective Geometry, Volume 1

Oswald Veblen, John Wesley Young - Geometry, Projective - 1910 - 355 pages
...into lines by equations of the form (1) B = a 3l x 1 where the determinant A of the coefficients a {j is different from zero. Conversely, every transformation...corollary we have COROLLARY 1. The transformation pu[~x^ pu! 2 ~ x 2 , pu^== x 3 in a plane represents a polarity in which to every side of the triangle...
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Fourteen Papers on Logic, Algebra, Complex Variables and Topology

1965 - 404 pages
...elements xv . . . , Xrt, satisfying the conditions p^j-...-p^.o, *&-..*n *0. Then g(E, B, F, p) > o + 1. The proof of this theorem is completely analogous to the proof of Theorem 4 of the note [1]. 5. Universal principal fiber spaces of genus n. Suppose that G is a topological...
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Twelve Papers on Functional Analysis and Geometry

Mathematics - 1969 - 270 pages
...then (1 - \A) 1 is an integral operator- function of order not greater than r and of minimal type. The proof of this theorem is completely analogous to the proof of Theorem 2.1. In this connection it is necessary to consider only that for the conditions of the theorem det(l...
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Six papers in analysis, Volume 101

Boris Moiseevich Levitan Vladimir Aleksandrovich Marchenko Boris Leonidovich Rozhdestvenski_ - 1973 - 260 pages
...^{¿2¿ift2fti} (A2 = °° '/ A , = °°) /sa transformation operator defined on the set *JDf |'0 e). The proof of this theorem is completely analogous to the proof of Theorem 3.1.1, and is omitted. We observe only that from the proof of Theorem 3.1. Г it follows that the transformation...
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Some Questions in Constructive Functional Analysis, Issues 113-114

Phan Dình Diêu - Mathematics - 1974 - 236 pages
...and T'separated. 4.2.1. If a locally convex space 3DÎ is enumerably normable, then it is metrizable. The proof of this theorem is completely analogous to the proof of the corresponding theorem in classical functional analysis (see, for example, [7], Chapter XI). Now...
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Symbolic and Algebraic Computation: International Symposium ISSAC' 88, Rome ...

Patrizia Gianni - Computers - 1989 - 564 pages
...Euler product. Theorem 4 Co, = flp(1 _ ¿)1, where the product is taken over all prime ideals P in O¿. The proof of this theorem is completely analogous to the proof of Theorem 2. Finally if we define ¿t for O¿ as we did for Z, we get the following inversion theorem. Theorem...
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Eight Papers on Differential Equations and Functional Analysis

Differential equations - 1966 - 304 pages
...or 6* ; f. Im A, (a) = 0 only for a = a. or only for a = h., and at that point A'Дff) = -tan1¿°. The proof of this theorem is completely analogous to the proof of Theorem 5. After this the prohlem of ohtaining asymptotics for E(x, y) in a neighhorhood of a special direction...
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Transactions of the Moscow Mathematical Society

American Mathematical Society - Mathematics - 1968 - 382 pages
...Incapacity (a> n - 2m) is as small as we please, so that u turns out to be continuous on the remaining set. The proof of this theorem is completely analogous to the proof of Luzin's Theorem and proceeds by means of Lemma 1.8. (3.1) (G)' where C does not depend on u. This inequality...
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Eleven Papers on Analysis

Mathematical analysis - 1966 - 292 pages
...the classes KR or К(ш). Then the operator Jc0 is bounded from below in ij^m^ and s(£0)=[0, т). The proof of this theorem is completely analogous to the proof of Theorems 3.1 and 3.3 and teduces to a reference to Theorems 1.1, 1.2, 2.2 and 2.3. We now have an analog...
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Theory of Entire and Meromorphic Functions: Deficient and Asymptotic Values ...

Guan-hou Zhang - Mathematics - 1993 - 394 pages
...the above hypothesis, there exists a curve L tending continuously to oo in region Dp , such that lim The proof of this theorem is completely analogous to the proof of Theorem 4. 14 in the sequel. §4.2. The Denjoy Conjecture 4.2.1. The Denjoy Conjecture. In 1907, A Denjoy made...
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