Projective Limits via Inner Premeasures and the True Wiener Measure
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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.
Mathematics Subject Classification (2000).28A12 28A35 28C20 60A10
Keywords.Projective limit theorems of the Prokhorov and Kolmogorov types Prokhorov condition Inner premeasures and their inner extensions Direct and inverse images of inner premeasures Transplantation theorems Wiener measure and Wiener premeasure Brownian convolution semigroup
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