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In the paper Edge analysis and identification using the continous shearlet transform (by K. Guo, D. Labate and W. Lim) I encountered the term smooth partition of a set. I do not understand the term smooth partition Lets be precise what is written:

[...]let $\Omega$ be a bounded open subset of $R^2$ and assume a smooth partition $\Omega=\cup_n(\Omega_n \cup \Gamma)$, where [...]

now there are severel requirements listed. To be clear, I know what a partition is, but I only know the term smooth in the sense of a smooth function. Thanking you in anticipation.

Chris S.
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  • I think the "smooth" is used here because the partition is defined such that each boundary is generated by the $C^3$ curve. In many cases, a sufficient regular boundary is needed in the proof. – Q-Y Jul 02 '18 at 09:37
  • Thanks for your answer. I guess this makes sense. I do not see a "deeper" meaning neither. – Chris S. Jul 02 '18 at 09:43

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