In mathematics, the Baker–Campbell–Hausdorff formula is the solution to the equation
Z
=
log
(
e
X
e
Y
)
{\displaystyle Z=\log {\big (}e^{X}e^{Y}{\big )}}
for possibly noncommutative X and Y in the Lie algebra of a Lie group. This formula tightly links Lie groups to Lie algebras by expressing the logarithm...
Consider a smooth convex/compact domain $D\subset \mathbb{R}^n$ and a smooth, concave function $F:D\to \mathbb{R}$. Then we can define the function that simply takes the volume of the upper contour sets determined by the argument:
$$G(t) = \int_{\{x\in D \; : \; F(x) \ge t\}} d\lambda$$
where ...
