2019/09/08 by Oleksii Mostovyi, Mostovyi, Oleksii, Pietro Siorpaes +1
Economics, Econometrics and Finance · Mathematics · #28A15 #28A25 #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Stochastic processes and financial applications #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.1909.03505
openalex publication_date 2019/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given positive measures \ν,\μ on an arbitrary measurable space (\Ω,\n mathcal F), we construct a sequence of finite partitions (\πn)n of\n(\Ω, mathcal F) s.t.
sumA
in
pin:
mu(A)gt;0 1A\n
frac
nu(A)
mu(A)
longrightarrow
fracd
nuad
mu
quad
mu
text a.e.\nas n
to
infty . As an application, we modify the probabilistic proof of\nthe Radon-Nikodym Theorem so that it uses convergence along a properly chosen\nsequence (instead of along a net), and so that it does not rely on the\nmartingale convergence theorem (nor any probability theory), obtaining a\ncompletely elementary proof.\n