On generalized Csiszár-Kullback inequalities

Andreas Unterreiter*, Anton Arnold, Peter Markowich, Giuseppe Toscani

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

66 Scopus citations


Classical Csiszár-Kullback inequalities bound the L1-distance of two probability densities in terms ot their relative (convex) entropies. Here we generalise such inequalities to not necessarily normalized and possibly non-positive L1 functions. Also, we analyse the optimality of the derived Csiszár-Kullback type inequalities and show that they are in many important cases significantly sharper than the classical ones (in terms of the functional dependence of the L1 bound on the relative entropy). Moreover our construction of these bounds is rather elementary.

Original languageEnglish (US)
Pages (from-to)235-253
Number of pages19
JournalMonatshefte fur Mathematik
Issue number3
StatePublished - Jan 1 2000


  • Generalized Csiszár-Kullback inequalities
  • Relative (convex) entropies

ASJC Scopus subject areas

  • Mathematics(all)


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