Sur les fonctions convexes et les inégalités entre les valeurs moyennes¶
Jensen, J. L. W. V. (1906). Sur les fonctions convexes et les inégalités entre les valeurs moyennes. Acta Mathematica, 175-193.
Cited by¶
2 citations across 2 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Antifragility
- The property is dose-dependent and curvature-dependent: it holds within a tolerance window beyond which the same stressors that strengthen become destructive, a non-linearity Jensen's inequality makes precise for any convex transformation of a fluctuating input.
This sourceEstablishes Jensen's inequality for convex functions, E[f(x)] ≥ f(E[x]); the basis for why increasing the variance of a fluctuating input raises the expected output of a convex response at fixed mean (and lowers it for a concave one), making antifragility's dose-/curvature-dependence precise.
- The property is dose-dependent and curvature-dependent: it holds within a tolerance window beyond which the same stressors that strengthen become destructive, a non-linearity Jensen's inequality makes precise for any convex transformation of a fluctuating input.
Mechanisms¶
- Inter-Event Interval Estimator
- Because the estimate is the reciprocal of a single noisy interval, one missing or spurious event corrupts it completely, and — more insidiously — averaging reciprocals systematically overstates the rate
This sourceFor positive varying intervals, Jensen’s inequality establishes that the mean reciprocal exceeds the reciprocal of the mean.
- Because the estimate is the reciprocal of a single noisy interval, one missing or spurious event corrupts it completely, and — more insidiously — averaging reciprocals systematically overstates the rate
Verification¶
Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.
Does it back the claim? Not recorded. Neither this nor any other of the 2 citations of this work carries a recorded support check.
Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.
See how references were verified.
Registry ID ref:3658beca7279 · see in the full table