Abstract
In this article, we prove the following statement that is true for both unbounded and bounded Vilenkin systems: for any ε ∈ (0,1), there exists a measurable set E ⊂ [0,1) of measure bigger than 1 — ε such that for any function f ∈ L1 [0,1), it is possible to find a function g ∈ L1 [0,1) coinciding with f on E and the absolute values of non zero Fourier coefficients of g with respect to the Vilenkin system are monotonically decreasing.
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