# Questions tagged [integral-inequality]

For questions inequalities which involves integrals, like Cauchy-Bunyakovsky-Schwarz or Hölder's inequality. To be used with (inequality) tag.

912 questions
Filter by
Sorted by
Tagged with
41 views

25 views

### Inequality for joint probabilities of dependent random vectors

Let $X$ and $Y$ be two dependent random vectors in $\mathbb{R}^d$, such that $X\neq Y$ with probability 1, whose joint probability measure has density $\mu(x,y)$ with respect to the Lebesgue measure. ...
25 views

### References for variants of Jensen inequality

I am looking for a reference for the following claim: Let $X$ be a probability space, and let $g:X \to \mathbb [0,\infty)$ be in $L^1(X)$. Let $\phi:\mathbb [0,\infty) \to [0,\infty)$ be convex and ...
148 views

37 views

### Need help in proving a version of Stirling Formula

I am trying to prove this inequality but unable to do so -> $log(n!) \leq \int_2^{n+1} log(x) dx$ . My attempt -> using Stirling Formula LHS = n log(n) - n + O ( log(n) ) and Integral is n( log(n+...
I am asking if an argument which I am trying to use make sense or not Assume $I(z) = \int_0^1 f(x)^n 1/x^2 \, dx$ then I wrote $\lim_{n \to \infty} I(z)^{1/n} \leq \int_0^1 f(x) \, dx$ , assuming ...