Denote by $\theta$ the angle at $x$ that is common to these triangles.
The following lemma, crucial to Theorem 2, is also implicit in [4].
Knowing this matrix is equivalent to knowing the multiplicities of the $l_i$.
Thus $\theta$ will be less than $\pi$ by an amount comparable to $a(s)$.
Essential to the proof are certain topological properties of $G$.
We shall see later that the values of $h(n)$ for large $n$ are irrelevant to the problem.
We base our development on two properties of prolongation peculiar to this case.
But the $T_n$ need not be contractions in $L^1$, which is the main obstruction to applying standard arguments for densities.
We write $\beta= ......$, which is a slight modification to the previous version of $\beta$.
We can join $a$ to $b$ by a path $\pi$. [Not: “join $a$ with $b$”]
The case where $i$ is odd yields to a similar argument.
Exercises 2 to 5 [= Exercises 2--5; amer. Exercises 2 through 5]
To deal with (3), consider ......
We now apply (2) to get $Nf=0$.
Theorems 1 and 2 combine to give the following result.
To see that $f=g$ is fairly easy.
Every prime in the factorization appears to an even power.
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