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Projective limits via inner premeasures and the true Wiener measure

In: Measure and Integration

Author

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  • Heinz König

    (Universität des Saarlandes, Fakultät für Mathematik und Informatik)

Abstract

The paper continues the author’s work in measure and integration, which is an attempt at unified systematization. It establishes projective limit theorems of the Prokhorov and Kolmogorov types in terms of inner premeasures. Then it specializes to obtain the (one-dimensional) Wiener measure on the space of real-valued functions on the positive halfline as a probability measure defined on an immense domain: In particular the subspace of continuous functions will be measurable of full measure - and not merely of full outer measure, as the usual projective limit theorems permit to conclude.

Suggested Citation

  • Heinz König, 2012. "Projective limits via inner premeasures and the true Wiener measure," Springer Books, in: Measure and Integration, edition 127, pages 273-312, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-0382-3_13
    DOI: 10.1007/978-3-0348-0382-3_13
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