Theorems · Definition · number theory

AbstractMeasure.toCLMEquiv

{X : Type u_1} →
  {R : Type u_3} →
    {E : Type u_4} →
      [inst : TopologicalSpace X] →
        [inst_1 : AddCommGroup E] →
          [inst_2 : TopologicalSpace E] →
            [inst_3 : IsTopologicalAddGroup E] →
              [inst_4 : CommRing R] →
                [inst_5 : TopologicalSpace R] →
                  [inst_6 : IsTopologicalRing R] →
                    [inst_7 : Module R E] → [inst_8 : ContinuousSMul R E] → AbstractMeasure X R E ≃ₗ[R] C(X, R) →L[R] E

The defining equivalence between measures and continuous linear maps on continuous functions.

Defined in

Mathlib.NumberTheory.Padics.Measure.Basic

Cited by

2 results in Mathlib

Foundations

Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceAddCommGroupTopologicalSpaceIsTopologicalAddGroupCommRingTopologicalSpaceIsTopologicalRingModuleContinuousSMul