Open AccessA New Approach to the Lebesgue-Radon-Nikodym Theorem. with respect to Weighted p-adic Invariant Integral on ℤp
Author(s) -
Seog-Hoon Rim,
Joohee Jeong
Publication year - 2012
Publication title -
kyungpook mathematical journal
Language(s) - English
Resource type - Journals
eISSN - 1225-6951
pISSN - 0454-8124
DOI - 10.5666/kmj.2012.52.3.299
Subject(s) - mathematics , lebesgue integration , invariant (physics) , pure mathematics , lebesgue–stieltjes integration , discrete mathematics , riemann integral , fourier integral operator , mathematical physics , operator theory
We will give a new proof of the Lebesgue-Radon-Nikodym theorem with respect to weighted p-adic q-measure on , using Mahler expansion of continuous functions, studied by the authors in 2012. In the special case, q = 1, we can derive the same result as in Kim, 2012, Kim et al, 2011.
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