in the previous chapter [= in the immediately preceding one]
in a previous chapter [= in an earlier chapter]
This is in agreement with our previous notation.
In this chapter we shall depart from the previous notation and use the letter $m$ not for Lebesgue measure, but for Lebesgue measure divided by $(2\pi)^{1/2}$.
Analysis of the proofs of these previous results shows that ......
We now apply the previous observation to estimate $F$.
The primary advance is to weaken the assumption that $H$ is $C^2$, used by previous authors, to the natural condition that $H$ is $C^1$.
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