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Inequalities for the Mean Concentration
1985We shall now prove the two inequalities mentioned in section 4. In the proofs we rely on Jensen’s inequality for convex functions. A function f is called convex if all its cords lie above or on the graph of f. In analytical terms this means that $$pf({x_{1}}) + \left( {1 - p} \right)f\left( {{x_{2}}} \right) \geqslant f\left( {p{x_{1}} + \left( {1 -
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A Sharper Form of the Inequality for the Concentration Function
Theory of Probability & Its Applications, 1979A. A. Yudin, L. P. Postnikova
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