Lebesgue Points and Precise Representatives for $L^p$ Functions Geometric Measure Theory Approximate Gradient Identifies $D^a u$ Geometric Measure Theory Hardy-Littlewood Maximal Inequality Geometric Measure Theory BV Sobolev Inequality Geometric Measure Theory BV Extension Theorem Geometric Measure Theory Portmanteau Theorem for Radon Measures Geometric Measure Theory Almost Every Point Is a Lebesgue Point Geometric Measure Theory Area Formula for Smooth Graphs Geometric Measure Theory