Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Commensurable and the stronger one?

  1. Oct 23, 2008 #1
    i have the next metrics on the $C^1 \left[ {0,T} \right]$ space

    \ d_\infty (x,y) = \sup {\rm{ metric}} \\
    d_2 (x,y) = \left\{ {\int_0^T {\left[ {x(t) - y(t)} \right]^2 dt} } \right\}^{1/2} \\
    d_3 (x,y) = \left\{ {\int_0^T {\left| {x(t) - y(t)} \right|^3 dt} } \right\}^{1/3} \\
    d(x,y) = d_\infty (x,y) + d_\infty (\dot x,\dot y),{\rm{ where }}\dot x = \frac{{dx}}{{dt}}

    each one generate a topology in that space (\[T_\infty\], \[T_\2\], \[T_\2\],\[T_\0\] )

    the questions are, which of them are commensurables?
    if there are 2 commensurables which is the stronger one?

    Note that the metrics are equivalet...
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted

Similar Discussions: Commensurable and the stronger one?
  1. Struggling on this one (Replies: 1)

  2. Proof of this one (Replies: 11)

  3. One-to-One Functions (Replies: 7)

  4. One theorem (Replies: 10)

  5. One-to-One Mapping (Replies: 6)