Sigma-Algebra Definition Error in Derivatives of Interpolating Polynomials Numerical Analysis Boundedness Theorem Continuity Weak Lower Semicontinuity of Convex Functionals Analysis Identification with Sobolev Spaces Analysis Divided Differences and Derivatives Numerical Analysis Lower Semicontinuity Of Total Variation Geometric Measure Theory Dominated Convergence Theorem Measure Theory Properties of Connected Components Topology Analysis Area Measure Theory Subarea