∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : InnerProductSpace ℝ E] [inst_2 : MeasurableSpace E]
  [inst_3 : BorelSpace E] {μ : MeasureTheory.Measure E} {F : Type u_2} [inst_4 : NormedAddCommGroup F]
  [inst_5 : InnerProductSpace ℝ F] [inst_6 : MeasurableSpace F] [inst_7 : BorelSpace F] [SecondCountableTopology F]
  [inst_9 : CompleteSpace F] [inst_10 : CompleteSpace E] [MeasureTheory.IsFiniteMeasure μ],
  MeasureTheory.MemLp id 2 μ →
    ∀ (L : E →L[ℝ] F) (u v : F),
      ((ProbabilityTheory.covarianceBilin (MeasureTheory.Measure.map (⇑L) μ)) u) v =
        ((ProbabilityTheory.covarianceBilin μ) ((ContinuousLinearMap.adjoint L) u)) ((ContinuousLinearMap.adjoint L) v)