Abstract
We prove that if 1<p<infty and delta :]0,p-1]rightarrow ]0,infty [ is continuous, nondecreasing, and satisfies the Delta _2 condition near the origin, then This result permits to clarify the assumptions on the increasing function against the Lebesgue norm in the definition of generalized grand Lebesgue spaces and to sharpen and simplify the statements of some known results concerning these spaces.
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