Could you help me, please.
Is there any basis $f_i$ for any general enough (may be $C^\infty$) class of "smooth" functions $[0;1]^n \rightarrow R$, for which it is possible to analytically estimate the measure (surface) of any finite sum $g(.) = \sum A_i f_i(.)=0$ ?
By the surface I mean the basic measure $\oint_{g(.)=0} 1 dS$.
In 2D case it means that for any linear combination of those functions it is possible to analytically estimate the length of the curve(s) which separate the positive and the negative values of the function on $[0;1] \times [0;1]$.
In 3D case we'd talk about surface(s) separating volumes and so on.
I do not need to estimate the form of the surface, only its measure.
Is there such a useful basis or can it be constructed?
Thank you.