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Verein (to appear). f In the Anglo-American literature, the method is called Gram-Schmidt process in honor of the Danish mathematician Johann P. Gram, who was first to recognize the importance of orthonormal systems of functions. D. from the University of Copenhagen in 1879. He joined the life insurance company Hafnia in 1875 and became vice president in 1896. He was president of the accident insurance company Skold at the time of his death in 1916. In his publication "Ueber die Entwickelung reeller Functionen in Reihen mittelst der Methode der kleinsten Quadrate," / .

Every suck interval is a lattice. " EXAMPLES OF HILBERT* SPACES. Example 1. 43) is a Hilbert space. 7 is a Hilbert space (see Natanson [54], p. 186). Example 2. 7 with the scalar * David Hilbert, probably the most distinguished German mathematician besides Gauss, was born Jan. 23, 1862, in Königsberg. D. o. Professor) in 1892. In 1895 he went to Göttingen, where he stayed until his death, Feb. 14, 1943. Obituary by G. Hamel, Z. Angew. Math. Mech. 23, 128 (1943). + Henri Leon Lebesgue, son of a typesetter, was born June 28, 1865, in Beauvais, France.

Then let h be an element of the sphere S(g, -^δ). 8) we have | p{h, k) — p(g> k)\ < ^δ for all k e R; hence this is true for the infima also: \p(h9A)-p{g,a)\^fa \P(h)B)-p(giB)\^iSi and, therefore, p(hf B) — p(hy A) > δ — ^δ — ^δ = ^δ, that is, he M. M is, therefore, an open set and hence a neighborhood of A. Similarly, N is a neighborhood of B and R is normal. ) EXAMPLES OF TOPOLOGICAL SPACES. ) Example 1. The following three spaces are topological ones, but not Haussdorff spaces. The elements of the space R are in each case 24 I.

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