An elementary construction of the Wiener measure

2020/11/11 by R. P. Pakshirajan, Pakshirajan, R. P., M. Sreehari +1
Mathematics · #60G15 #60J65 #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical and Theoretical Analysis #Probability (math.PR) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2011.05584

openalex publication_date 2020/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Our construction of the Wiener measure on \mathfrakC consists in first defining a set function φ on the class of all compact sets based on certain n-dimensional normal distributions, n = 1, 2,… using the structural relation at (1) below. This structural relation, discovered by the first author, is recorded in his book [2] on page 130. We then define a measure μ on the Borel σ-field of subsets of C which is the Wiener measure.

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