Roitman's combinatorial principle $\Delta$ is equivalent to monotone normality of the nabla product, $\nabla (\omega +1)^\omega$. If $\{ X_n : n\in \omega\}$ a family metrizable spaces and $\nabla_n X_n$ monotonically normal, then hereditarily paracompact. Hence, if holds box product $\square +1)^\omega$ Large fragments hold in $\mathsf{ZFC}$, yielding large subspaces (\omega+1)^\omega$ that ar...

The energy test of multivariate normality is an affine invariant based on a characterization equal distributions by distance. statistic degenerate kernel V-statistic, which asymptotically has sampling distribution that Gaussian quadratic form under the null hypothesis normality. parameters limit are eigenvalues integral operator determined Although Monte Carlo approach provides excellent approx...