Every measurable function on [a, b] is continuous after restriction to a closed set whose complement has arbitrarily small measure. Equivalent on ℝⁿ via the Tietze extension: measurable ≈ continuous on a large closed set.
Every measurable function on [a, b] is continuous after restriction to a closed set whose complement has arbitrarily small measure. Equivalent on ℝⁿ via the Tietze extension: measurable ≈ continuous on a large closed set.