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.

中文翻译：

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关于广义大Lebesgue空间中反对Lebesgue范数的因素

我们证明，如果\（1 <p <\ infty \）和\（\ delta：] 0，p-1] \ rightarrow] 0，\ infty [\）是连续的，并且不会减小，并且满足\（\ Delta _2 \）条件接近原点，然后

该结果可以阐明在广义大Lebesgue空间的定义中针对Lebesgue规范的递增函数的假设，并可以简化和简化有关这些空间的某些已知结果的表述。