https://math.codidact.com/categories/41/tags/6436.rssNew Posts Tagged 'Jensen's-inequality' - MathematicsMathematics - Codidact2022-02-11T21:32:00Zhttps://math.codidact.com/posts/285819Is it impossible to prove Jensen's inequality by way of step functions?whybecauseâ€https://math.codidact.com/users/550222022-02-04T01:03:31Z2022-02-11T21:32:00Z<p>Jensen's Inequality: Let $\varphi:\Bbb R\to \Bbb R$ be convex, and $f:[0,1]\to\Bbb R$ be integrable, and suppose $\varphi\circ f$ is integrable over [0,1]. Then
$$ \varphi\left(\int_{[0,1]} f\...