fpvandoorn/carleson
Source indexedlemma · leanprover/lean4:v4.32.0
MeasureTheory.measureReal_ball_le_same
Carleson.ToMathlib.MeasureTheory.Measure.IsDoubling · Carleson/ToMathlib/MeasureTheory/Measure/IsDoubling.lean:353 to 365
Mathematical statement
Exact Lean statement
lemma measureReal_ball_le_same (x : X) {r s r' : ℝ} (hsp : 0 < s) (hs : r' ≤ s * r) :
μ.real (ball x r') ≤ As A s * μ.real (ball x r)Complete declaration
Lean source
Full Lean sourceLean 4
lemma measureReal_ball_le_same (x : X) {r s r' : ℝ} (hsp : 0 < s) (hs : r' ≤ s * r) : μ.real (ball x r') ≤ As A s * μ.real (ball x r) := by have hz := measure_ball_le_same (μ := μ) x hsp hs have hbr': μ (ball x r') ≠ ⊤ := by finiteness have hbr: μ (ball x r) ≠ ⊤ := by finiteness have hAs : (As A s: ℝ≥0∞) ≠ ⊤ := by finiteness rw [← ENNReal.ofReal_toReal hbr, ← ENNReal.ofReal_toReal hbr', ← ENNReal.ofReal_toReal hAs, ← ENNReal.ofReal_mul] at hz · simp only [coe_toReal] at hz rw [← ENNReal.ofReal_le_ofReal_iff] · exact hz positivity · simp only [coe_toReal, zero_le_coe]