The way I understand level set functions is that you have a function U ,in a multidimentional space that can take values in some range and you ask about the
lebesque measure (multidimentional volume) v of the region where U is less than a value e.If you know this function v(e) you can use it in probabilistic arguments and computations.What is the U in your case and how do you compute v(e)?
Let me start defining what I call set function: it is a number associated not to a numerical variable or n numerical variable but to a set. We define a set function by computing (no matter what is the model from which we extract a probability) the set around one particle which contains the maximum probability to have in that set only one particle. This is a domain in real space which we can draw easily and that is what is done in our paper. I hope this answers your question. Regards, GC
@Giovani Ciccoti.Thanks for the clarification.I understand now that your definition is not that of level set function,but more related to concepts of
scaled particle theory and( if I remember well the name) Hertz distributions.
Dikeos Mario
Right. I didn't know what are Hertz distributions but I found a Paper by Torquato (of 1989) and so I understood that you got the point!
Best GC
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