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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

Canonical source
Full Lean sourceLean 4
lemma measureReal_ball_le_same (x : X) {r s 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: 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]