[SciPy-User] [OT] Transform (i.e., Fourier, Laplace, etc.) methods in Prob. & Stats.

David Cournapeau david@ar.media.kyoto-u.ac...
Wed Nov 25 22:45:45 CST 2009


josef.pktd@gmail.com wrote:
>
> Maybe the last statement is wrong, it's too long ago that I
> struggled with this. Maybe I'm mixing up Lebesgue-integral,
> Lebesgue-measurable, and measures that are absolutely continuous
> with respect to Lebesgue-measure.
>   

I am by no mean an expert on this, but I believe you are right. AFAIK,
contour integrals require to have a piecewise-continuous parametrization
of your path, and for me, the whole point of Lebesgue integrals is to
handle cases where the set over which you integrate the function is not
a (finite) union of intervals.

I don't know if it makes sense to define something "like" contour
integrals for lebesgue integrals. The fundamental reason why Lebesgue
integrals work the way they do is because for a function f: E ->F, only
the properties of F (and how the inversion function maps elements of the
sigma algebra F) matter. And complex analysis is 'special' because of
the special structure of E, not F.

David


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