Foundations of Constructive Analysis

approximation arbitrarily arbitrary Assume B₁ Banach algebra Banach space Borel set bounded linear functional bounded subset called Cauchy sequence Chap Choose compact interval compact set complemented set complete complex numbers Consider continuous function converges convex Corollary countable defined Definition dense differentiable function element equal equivalent everywhere f and g f₁ finite fn(x follows function f Hence inequality integer integrable function integrable set L₁(G L₂(G Lemma Let f locally compact space martingale measurable functions metric space modulus of continuity mutually singular neighborhood nonnegative normed linear space null set open set operator path positive constant positive integer Proof Let Proposition prove rational numbers real numbers satisfied seminorm sequence f simple function test function Theorem totally bounded U₁ uniformly continuous vector Write X₁ αμ