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Definition of a Measure in Hubert Space

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Integration in Hilbert Space

Part of the book series: Ergebnisse der Mathematik und ihrer Grenzgebiete ((MATHE2,volume 79))

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Abstract

Let X be a real separable Hilbert space with elements x, y, z, etc. Real numbers will be designated by small Greek letters; α x + β y and (x, y) will denote, as usual, the operations of multiplication of a vector (element of X) by a scalar, vector addition and the scalar product of vectors The norm of a vector will be designated by

$$ \left| x \right| = \sqrt {{(x,x)}} $$

Subsets of X will be denoted by large Latin letters, classes of subsets by large Gothic letters. A class of sets A in which we allow the operations of set difference, union and intersection is called a ring. A ring of sets A containing X as an element is called an algebra. An algebra of sets in which the union operation can be applied countably many times is called a σ-algebra.

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© 1974 Springer-Verlag Berlin Heidelberg

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Skorohod, A.V. (1974). Definition of a Measure in Hubert Space. In: Integration in Hilbert Space. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 79. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-65632-3_1

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  • DOI: https://doi.org/10.1007/978-3-642-65632-3_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-65634-7

  • Online ISBN: 978-3-642-65632-3

  • eBook Packages: Springer Book Archive

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