Principal Subspace Error Bound for Sub-Gaussian Sample Covariance Matrices Probability & Statistics Finite-Rank BBP Outlier Location Theorem for Spiked Covariance Matrices Probability & Statistics Existence of Nonmeasurable Subsets of the Real Line Probability & Statistics Law of Total Variance Probability Theory $L^2$ Integrability Implies $L^1$ Integrability Probability Theory Tensorization Theorem for Logarithmic Sobolev Inequalities Probability & Statistics Conditional Convergence Theorems Conditional Expectation Equivalence of Squared-Loss Restricted Strong Convexity and Restricted Eigenvalues Probability & Statistics Probability & Statistics Area