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Thread: integral geometric measure

  1. #1
    Dec 2009

    integral geometric measure

    $\displaystyle \sideset{}{_\theta}\prod$ is the orthogonal projection onto the line Lθ passing through the origin that makes an angle θ with the horizontal.
    It's description is
    "Count the number of intersections of a given set F with a straight line, and then integrate this number over the space of all lines."

    But I think $\displaystyle \sideset{}{_\theta^{-1}}\prod$(y) is not a straight line and $\displaystyle \sideset{}{_\theta^{-1}}\prod$ is a set containing set F.
    Also, I see there is only one staight line Lθ here.

    What 's wrong in my thought?

    (additional question: When F is a rectifiable curve, I1(F) is twice its length.Why?)
    Last edited by ldpsong; Apr 6th 2010 at 08:56 AM.
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