property of Hamel bases
$begingroup$
Let $H$ be a $mathbb{Q}$-basis of $mathbb{R}$ (Hamel basis).
It is known, that $H$ is dense in some interval, also is measurable with measure $0$ or nonmeasurable with infinite outer measure.
Let $H_1,H_2$ be two Hamel bases and $D=H_1-H_2={h_1-h_2colon h_1in H_1, h_2in H_2}$.
Are there are any known facts about the measure of $D$ - e.g. $D$ is nonmeasurable or contains an interval or maybe has infinite outer measure?
real-analysis hamel-basis
edited Dec 26 '18 at 19:29
José Carlos Santos
168k22132236
asked Jan 15 '18 at 0:04
user502959user502959
22718
$endgroup$
add a comment |
$begingroup$
Let $H$ be a $mathbb{Q}$-basis of $mathbb{R}$ (Hamel basis).
It is known, that $H$ is dense in some interval, also is measurable with measure $0$ or nonmeasurable with infinite outer measure.
Let $H_1,H_2$ be two Hamel bases and $D=H_1-H_2={h_1-h_2colon h_1in H_1, h_2in H_2}$.
Are there are any known facts about the measure of $D$ - e.g. $D$ is nonmeasurable or contains an interval or maybe has infinite outer measure?
real-analysis hamel-basis
edited Dec 26 '18 at 19:29
José Carlos Santos
168k22132236
asked Jan 15 '18 at 0:04
user502959user502959
22718
$endgroup$
add a comment |
$begingroup$
Let $H$ be a $mathbb{Q}$-basis of $mathbb{R}$ (Hamel basis).
It is known, that $H$ is dense in some interval, also is measurable with measure $0$ or nonmeasurable with infinite outer measure.
Let $H_1,H_2$ be two Hamel bases and $D=H_1-H_2={h_1-h_2colon h_1in H_1, h_2in H_2}$.
Are there are any known facts about the measure of $D$ - e.g. $D$ is nonmeasurable or contains an interval or maybe has infinite outer measure?
real-analysis hamel-basis
edited Dec 26 '18 at 19:29
José Carlos Santos
168k22132236
asked Jan 15 '18 at 0:04
user502959user502959
22718
$endgroup$
Let $H$ be a $mathbb{Q}$-basis of $mathbb{R}$ (Hamel basis).
It is known, that $H$ is dense in some interval, also is measurable with measure $0$ or nonmeasurable with infinite outer measure.
Let $H_1,H_2$ be two Hamel bases and $D=H_1-H_2={h_1-h_2colon h_1in H_1, h_2in H_2}$.
Are there are any known facts about the measure of $D$ - e.g. $D$ is nonmeasurable or contains an interval or maybe has infinite outer measure?
real-analysis hamel-basis
real-analysis hamel-basis
edited Dec 26 '18 at 19:29
José Carlos Santos
168k22132236
asked Jan 15 '18 at 0:04
user502959user502959
22718
edited Dec 26 '18 at 19:29
José Carlos Santos
168k22132236
asked Jan 15 '18 at 0:04
user502959user502959
22718
edited Dec 26 '18 at 19:29
José Carlos Santos
168k22132236
edited Dec 26 '18 at 19:29
José Carlos Santos
168k22132236
edited Dec 26 '18 at 19:29
José Carlos Santos
168k22132236
168k22132236
asked Jan 15 '18 at 0:04
user502959user502959
22718
asked Jan 15 '18 at 0:04
user502959user502959
22718
asked Jan 15 '18 at 0:04
user502959user502959
22718
22718
add a comment |
add a comment |
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