Theorems · Theorem · measure theory

MeasureTheory.integral_pos_of_integrable_nonneg_nonzero

∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : TopologicalSpace α] [μ.IsOpenPosMeasure]
  {f : α → ℝ} {x : α}, Continuous f → MeasureTheory.Integrable f μ → 0 ≤ f → f x ≠ 0 → 0 < ∫ (x : α), f x ∂μ

Defined in

Mathlib.MeasureTheory.Integral.Bochner.Basic

Cited by

1 results in Mathlib

Foundations

Depth 257 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceMeasureTheory.Measure.IsOpenPosMeasure