∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : InnerProductSpace ℝ E] [inst_2 : MeasurableSpace E]
  [inst_3 : BorelSpace E] {μ : MeasureTheory.Measure E} [inst_4 : CompleteSpace E],
  ¬MeasureTheory.MemLp id 2 μ → ProbabilityTheory.covarianceOperator μ = 0