Foundations of Constructive Analysis

algebra approximation arbitrarily arbitrary Assume B₁ Banach space Borel set bounded linear functional bounded subset called Cauchy sequence Chap Choose classical compact interval compact set compact subset complemented set complete complex numbers compute Consider constructive continuous function converges convex Corollary countable defined almost everywhere Definition dense differentiable function element equivalent f and g f₁ finite follows function f Hence Hilbert space inequality integrable function integrable set L₁(G Lebesgue measure Lemma Let f locally compact space mathematics measurable functions metric space modulus of continuity neighborhood nonnegative nonzero normable linear functional normed linear space null set open set operators path positive constant positive integer principle of omniscience Proof Let Proposition prove rational numbers real numbers satisfied seminorm sequence f simple function test function Theorem totally bounded U₁ uniformly continuous vector Write αμ