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Thirdly, to push for measures to limit inequalities, such as the fact that some international business chiefs earn 240 times as much as an ordinary citizen.
Without loss of generality, we only verify the upper limit inequalities.
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Governments tax in order to fund public goods and limit inequality, but taxes are no free lunch.
However, instead of scrapping the 11-plus (the obvious way to maximise choice and limit inequality) tinkering around the edges is proposed.
These policies include methods to reduce resource use, limit inequality, fix the financial system, create meaningful jobs, and change the way we measure progress.
This inequality can be regarded as a limit inequality of (1.1) as p → ∞.
This inequality may be regarded as a limit inequality of (4.1) when p → ∞ (see Remark 4.3).
The limit inequality is valid for all functions in the Sobolev space H1.
The convergence of the constant, as the size of perforation tends to zero, to the constant in the limit inequality was proved.
But it is clear that it was known before and in his 1925 article [1] Hardy informed that Pólya had pointed out the fact that (4.3) is in fact a limit inequality (as p → ∞) of the inequality (1.1) for p > 1 and the proof is literally the same as that above that (4.1) implies (4.2).
However, it is reasonable to ask if the following (limit) inequality can hold for some K > 0 ∫ 0 1 ( 1 x ∫ 0 x f ( y ) d y ) p x p − 1 d x ≤ K ∫ 0 1 f p ( x ) x p − 1 d x. (3.1).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com