Distribution similar to PPP According to the definition of Poisson Point Process, I can't define a certain number of nodes which are distributed in an area as PPP. Is there a distribution (a certain number of nodes distributed in a restricted area) similar to PPP (An infinite number of nodes distributed in an infinite area)? 
 A: You can certainly restrict a Poisson point process to a finite region.  In a finite area, the number of points will be almost surely finite.  If you want 
to condition on the number of points being $n$, you just get $n$ independent points
uniformly distributed over the region. 
A: A more useful definition of a Poisson point field is: 
Let $\mu$ be a (finite or infinite) measure on a space $E$ with a sigma-algebra $\mathcal{B}$. To each set $A\in\mathcal{B}$ with $\mu(A)<\infty$, one assigns a r.v. $X(A)$ counting the number of Poissonian points in it. That random variable is supposed to have Poisson distribution with mean $\mu(A)$, and if $A_1,\ldots, A_n$ are mutually disjoint, then $X(A_1),\ldots,X(A_n)$ are supposed to be mutually independent.
The advantage of this definition is its generality. Also, you can clearly see how this definition is trivially preserved under constraining the space to subsets of $E$.
What you are talking about is the specific case case where the driving measure $\mu$ is Lebesgue or a multiple thereof.
