hope

1

This leaves the hope that a ratio theorem may persist in a more general setting.

2

[see also: expect, expectation]

A simple argument shows that we cannot hope to have $Df=0$.

We cannot hope to say anything about the structure of each isotropy factor as a system in its own right.

Almost everywhere convergence is the best we can hope for.

Specifically, one might hope that a clever application of something like Choquet's theorem would yield the desired conclusion.

If nothing else, I hope to convince my readers that Segal's theorem deserves recognition as a profound contribution to Gaussian analysis.

It is hoped that a deeper understanding of these residues will help establish new results about the distribution of modular symbols.



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