Foundations of Constructive Analysis

A₁ approximation arbitrarily arbitrary Assume B₁ Banach algebra Banach space Borel set bounded linear functional bounded subset Brouwer called Cauchy sequence Chap Choose compact interval compact set compact subset complemented set complete complex numbers consider constructive continuous function converges convex Corollary countable defined Definition dense differentiable function dµ(x dµ(y element equal equivalent exists finite follows function f ƒ and g Hence Hilbert space inequality integrable function integrable set L₁(G Lemma Let f locally compact space measurable functions metric space modulus of continuity neighborhood nonnegative normed linear space null set open set operators path positive constant positive integer positive measure Proof Let Proposition prove rational numbers real numbers satisfied sequence f simple function test function Theorem totally bounded U₁ uniformly continuous valid vector Write X₁ y₁