The proof is by induction on n.
For brevity, we drop the subscript t on ht.
Here H is a free R-module on as many generators as there are path components of X.
the amount the gambler wins on the nth play
However, A clearly has a topology T on it, namely,......
On making use of the bound...... we conclude that......
This bound is integrable and on integration one again obtains the same form of......
On restriction to B we have a homomorphism f:B→ C.
We establish our results both unconditionally and on the assumption of the Riemann Hypothesis.
The following example shows that the degree of smoothness predicted by Theorem 6 cannot be improved on.
We now show the following improvement on (2).
We now move on to the question of local normal forms.
Then (5) takes on the form...... [Or: takes the form]