Pollard books

Notes written by David Pollard for himself

In recent years I have written many small notes to keep a record for myself and to keep track of some things that interest me:

Some notes are just wrong or incomplete. Sometimes I got distracted and forgot to include bits and pieces scribbled on sheets of paper. The notes are not complete papers. Caveat lector. Please let me know if any links are broken---I often change the name of my files in an effort to remember their true purpose.

If you find any of these notes useful and decide to borrow some of the ideas it would be nice if you acknowledged the source.

The pdf files

Besicovitch
The main result generalizes the Vitali covering Lemma (UGMTP p68), leading to a differentiation theorem for Radon measures in euclidean spaces.
Ellipsoid
A rearrangement of Talagrand's construction of approximating sets for a gaussian process indexed by an ellipse. Might be included in Pttm chapter Majorizing.
MeasureIntegrals
An expanded version of Appendix A from my UGMTP book. It provides a self-contained account of the inner measure approach to the construction of measures. Some Sections are currently just placeholders for material that I intend to add someday.
Simplex
A rearrangement of Talagrand's construction of approximating sets for a gaussian process indexed by an a simplex.
SteinNormal
Notes made for discussion with Sekhar and Tim regarding multivariate extensions of Stein's method for establishing normal approximations. Mostly rearrangements and simplifications of matrerial from Stein's 1986 lecture notes.
Sudakov
A summary of the convex-geometric way to derive the Sudakov minoration for gaussians. Based on the accounts given by a few of my favorite authors.
[ICO]NameLast modifiedSizeDescription

[PARENTDIR]Parent Directory   -  
[   ]Besicovitch.pdf 2024-05-14 14:19 493K 
[   ]Ellipsoid.pdf 2024-08-01 13:30 292K 
[   ]MeasuresIntegrals.pdf 2022-02-06 15:34 1.0M 
[   ]Simplex.pdf 2024-06-15 17:15 280K 
[   ]SteinNormal.pdf 2023-06-03 14:19 373K 
[   ]Sudakov.pdf 2024-05-09 18:10 309K