Does there exist a set [tex]X\subset\mathbb{R}[/tex] that has a property(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

m^*(X\cap [0,x]) = \frac{x}{2},\quad\quad\forall x>0,

[/tex]

where [tex]m^*[/tex] is the Lebesgue outer measure?

My own guess is that this kind of X does not exist, but I don't know why. Anybody knowing proof for the impossibility of this X?

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Half of the real numbers, homogenously

Loading...

Similar Threads for Half real numbers | Date |
---|---|

I Complex integral of a real integrand | May 5, 2017 |

Half Range Series | Mar 7, 2015 |

Half wave fourier series help | Apr 18, 2012 |

Conformal mapping between two half space | Mar 20, 2012 |

Computing integrals on the half line | Feb 16, 2012 |

**Physics Forums - The Fusion of Science and Community**