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Diffstat (limited to 'ps2/main.tex')
| -rw-r--r-- | ps2/main.tex | 8 |
1 files changed, 5 insertions, 3 deletions
diff --git a/ps2/main.tex b/ps2/main.tex index 6979b97..17f7693 100644 --- a/ps2/main.tex +++ b/ps2/main.tex @@ -136,12 +136,14 @@ by considering its restriction to an increasing sequence of bounded rectangles: $K_n = \prod_{i=1}^n [-n, n]$. We can apply the previous result to each of the truncated distributions and again take the limit as $n\rightarrow\infty$. The validity of this last limit will depend on the exact technical assumptions we -make on $\mathbf{F}$ (basically we need $F$ to be quickly decreasing outside of -bounded intervals). +make on $\mathbf{F}$ (basically we need $\mathbf{F}$ to be quickly decreasing +outside of bounded intervals). More generally, the previous approach will apply as long as we are considering a distribution $\mathbf{F}$ in a space of distributions for which finite support distributions are dense for the weak topology. There are various -assumptions with various level of technicality which imply such a density. +assumptions with various level of technicality which imply such a density. We +can choose to apply one or the other based on the assumptions we have on +$\mathbf{F}$. \end{document} |