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Let $X_1,...,X_n$ be points on $\mathbb S^1.$ We then define the expectation value $E(X)=\frac{1}{n}\sum_{i=1}^n X_i.$ Let $\frac{dS(X_1)}{2\pi}$ be the normalized surface measure of $\mathbb S^1,$ i....

Looking at the generalizations of Stokes theorem, I did find a version for manifold with corners, but I was surprised this generalization doesn't contain a simple example such as the cone. So my ...