The multiple Cantelli inequalities

  • Haruhiko OgasawaraEmail author
Original Paper


The Cantelli inequality or the one-sided Chebyshev inequality is extended to the problem of the probability of multiple inequalities for events with more than one variable. The corresponding two-sided Cantelli inequality is extended in a similar manner. The results for the linear combination of several variables are also given as their special cases.


Probability inequality Chebyshev’s inequality Markov’s inequality Cauchy–Schwarz inequality Monotonic function Singular covariance matrix 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Otaru University of CommerceOtaruJapan

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