Some conditions for consistency and uniform consistency of statistical procedures

By C. Kraft. 1955

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The hardness of conditional independence testing and the generalised covariance measure (2018, background): “On the other hand, it is known that if a problem is untestable, the convex closure of the null must contain the alternative [31], [8], Theorem 5 and Corollary 1, resp.”
Some inequalities for information divergence and related measures of discrimination (2000, methodology): “Kraft [22] improved part of this by pointing out that 1 8V 2 ≤ h(1− 12h ) (follows by applying Cauchy–Schwartz’ inequality).”
On Pinsker's and Vajda's Type Inequalities for Csiszár's $f$ -Divergences (2006, background): “For instance, taking i) and we obtain that , ii) and (so that ) it follows that , and iii) and (so that ) we obtain that — see Kraft [45], cited in Dragomir et al. [34].”
Remarks on consistency of posterior distributions (2008, methodology): “A result of LeCam [21] shows that it is equivalent to the formulation of Schwartz involving an unbiased test for testing H0 : θ = θ0 vs.”