# Real analysis, measure theory after the Calculus

I want to get deeper into the real analysis and measure theory(in order to build good mathematical basis for learning stochastic proceses,probability theory etc.).

I want to ask you an advice about good real analyse's book: I have background in Single Variable Calculus and Multivariable calculus(Stewart's books). Linear Algebra(G.Strang book), Probability Theory and Inferential Statistics.

Which book will be the most appropriate variant for such background(I mean, it should me hard/informative enough, but not as hard, that it would destroy me).

• Do you know what $\limsup$ means? Do you know what uniform convergence means? How about metric spaces, countable vs uncountable sets, compactness, connectness, the Weierstrass approximation theorem, nowhere differentiable functions that are continuous? If not, then you will be well-advised to take a basic real analysis course first - the kind of course most students take before getting into measure theory. – zhw. Oct 5 '16 at 17:11
• @zhw. Thanks you for the advice! Can you please provide some good books for real analysis? – Daniel Yefimov Oct 5 '16 at 17:38