Model
Digital Document
Publisher
Florida Atlantic University
Description
We analyze some topics of the theory of integration in
infinite dimensional vector spaces. In the first five
chapters we deal mainly with I. E. Segal's approach to
integration in Hilbert spaces and prove the existence of
the canonical normal distribution in a Hilbert space;
we also give a simplified proof of Segal's version of the
Plancherel Theorem. In the last chapter we discuss a
theorem due to A. M. Gleason relevant to separable Hilbert
spaces. We deduce that the behavior of measures on finite
dimensional subspaces determines the behavior of the
measures in a separable Hilbert space.
infinite dimensional vector spaces. In the first five
chapters we deal mainly with I. E. Segal's approach to
integration in Hilbert spaces and prove the existence of
the canonical normal distribution in a Hilbert space;
we also give a simplified proof of Segal's version of the
Plancherel Theorem. In the last chapter we discuss a
theorem due to A. M. Gleason relevant to separable Hilbert
spaces. We deduce that the behavior of measures on finite
dimensional subspaces determines the behavior of the
measures in a separable Hilbert space.
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