Theorems · Theorem · measure theory

dimH_orthogonalProjectionOnto_le

∀ {𝕜 : Type u_6} {E : Type u_7} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  (K : Submodule 𝕜 E) [inst_3 : K.HasOrthogonalProjection] (s : Set E), dimH (⇑K.orthogonalProjectionOnto '' s) ≤ dimH s

The Hausdorff dimension of the orthogonal projection of a set s onto a subspace K is less than or equal to the Hausdorff dimension of s.

Defined in

Mathlib.Topology.MetricSpace.HausdorffDimension

Cited by

1 results in Mathlib

Foundations

Depth 214 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceSubmodule.HasOrthogonalProjection