Revision as of 14:23, 17 May 2019 edit 141.89.55.31 (talk) →Convergence in distribution: another way of defining the weak convergence implies an easy proof. ← Previous edit		Revision as of 14:28, 17 May 2019 edit undo 141.89.55.31 (talk) →Convergence in distribution: edited wrong maths symbol Tag: Visual edit Next edit →
Line 24: : <math> \mathbb E f(X_n) \to \mathbb E f(X)</math> for every bounded continuous functional ''f''. So it suffices to prove that <math> \mathbb E f(g(X_n)) \to \mathbb E f(g(X))</math> for every bounded continuous functional ''f''. Note that ''<math> F = f \circ g''</math> is itself a bounded continuous functional. And so the claim follows from the statement above. ===Convergence in probability===

Continuous mapping theorem: Difference between revisions