Hilbert Book Model Project/Slide S5

hbmp	Hilbert Book Model Project	S5
	We separate all point-like discontinuities from the domain $\mathrm{\Omega }$ by encapsulating them in an extra boundary
	$\underset{\mathrm{\Omega }-H}{\int }d\omega =\underset{\partial \mathrm{\Omega }\cup \partial H}{\int }\omega =\underset{\partial \mathrm{\Omega }}{\int }\omega -\sum _{k=1}^N\underset{\partial H_n^x}{\int }\omega$
	In fact, it is sufficient that $\partial H_n^x$ surrounds the current location of the elementary module
	We will select a boundary, which has the shape of a small cube of which the sides run through a region of the parameter spaces where the manifolds are continuous.
	If we take everywhere on the boundary the unit normal to point outward, then this reverses the direction of the normal on $\partial H_n^x$ which negates the integral
	Thus, in this formula, the contributions of boundaries $\{\partial H_n^x\}$ are subtracted from the contributions of boundary $\partial \mathrm{\Omega }$
	This means that $\partial \mathrm{\Omega }$ also surrounds the regions $\{\partial H_n^x\}$
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