# Find region given by Exists statement [closed]

I want to find, calculate its volume and visualize the following region most efficiently:

$\Gamma^\delta$ = { $\sigma$: $\exists \sigma' \in \Gamma$ with $F(\sigma,\sigma')\leq 1-\delta^2$}, where

-$\Gamma$ is a convex subset of the Ball with radius 1 (Bloch-sphere),

-$F(\sigma,\sigma')$ is some function where $\sigma$ and $\sigma'$ can be considered vectors in the Ball (actually they are single qubit density matrices and F is the Fidelity).

-$\delta$ is supposed to be small.

Since I'm more or less beginner with Mathematica I would be happy if somebody could give me some tips on that.

• This question will be easier to answer and more useful for others if you add a minimal working example of working code and data to show specifically what you are working with. Please edit your question to improve it. Include a minimum example of code that shows the problem and an example of the desired output. – rhermans Feb 16 '16 at 8:32