Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.mapRange_smul

∀ {α : Type u_1} {mα : MeasurableSpace α} {M : Type u_3} [inst : AddCommMonoid M] [inst_1 : TopologicalSpace M]
  {N : Type u_4} [inst_2 : AddCommMonoid N] [inst_3 : TopologicalSpace N] {R : Type u_5} [inst_4 : Semiring R]
  [inst_5 : Module R M] [inst_6 : Module R N] [inst_7 : ContinuousConstSMul R M] [inst_8 : ContinuousConstSMul R N]
  {v : MeasureTheory.VectorMeasure α M} {f : M →ₗ[R] N} (hf : Continuous ⇑f) {c : R},
  (c • v).mapRange f.toAddMonoidHom hf = c • v.mapRange f.toAddMonoidHom hf

Defined in

Mathlib.MeasureTheory.VectorMeasure.Basic

Cited by

1 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidTopologicalSpaceAddCommMonoidTopologicalSpaceSemiringModuleModuleContinuousConstSMulContinuousConstSMul