## The Annals of Probability

### Bounding $\bar{d}$-distance by informational divergence: a method to prove measure concentration

K. Marton

#### Abstract

There is a simple inequality by Pinsker between variational distance and informational divergence of probability measures defined on arbitrary probability spaces. We shall consider probability measures on sequences taken from countable alphabets, and derive, from Pinsker's inequality, bounds on the $\bar{d}$-distance by informational divergence. Such bounds can be used to prove the "concentration of measure" phenomenon for some nonproduct distributions.

#### Article information

Source
Ann. Probab. Volume 24, Number 2 (1996), 857-866.

Dates
First available in Project Euclid: 11 December 2002

http://projecteuclid.org/euclid.aop/1039639365

Digital Object Identifier
doi:10.1214/aop/1039639365

Mathematical Reviews number (MathSciNet)
MR1404531

Zentralblatt MATH identifier
0865.60017

#### Citation

Marton, K. Bounding $\bar{d}$-distance by informational divergence: a method to prove measure concentration. Ann. Probab. 24 (1996), no. 2, 857--866. doi:10.1214/aop/1039639365. http://projecteuclid.org/euclid.aop/1039639365.

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