Area of countable lines is suppose to be zero

lomos_lupin

Consider a plane with the normal axises and All of the horizontal and vertical lines which intersect the lines $y=0 \ and x=0$ in the rational points .

Prove that the area ,made of ,all of these Many lines is ZERO $0, \mathfrak 0$ Mr. Green

**Posted:** Sun Jan 29, 2006 7:52 am

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Megus

Well, I guess conclusion follows from the fact that value of Lebesgue integral of Dirichlet function is zero - if I understood correctly the statement you just have here two Dirichlet functions (rotated and translated of course) Smile

**Posted:** Mon Jan 30, 2006 9:26 am

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Przemyslaw Chojecki