Pointwise a.e. Convergence: Difference between revisions

Revision as of 06:56, 18 December 2020

Denote our measure space as $(X,{\mathcal {M}},\mu )$ .

Define the set $N=\{x:f(x)\neq \lim _{n\to \infty }f(x)\}$ .

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	Define the set <math>N = \{x: f(x) \neq \lim_{n \to \infty} f(x) \}</math>.		Define the set <math>N = \{x: f(x) \neq \lim_{n \to \infty} f(x) \}</math>.
	A sequence of measurable functions <math>\{f_n \}</math> converges to <math> f<\math>pointwise almost everywhere if <math> f_m (x) \to f(x)<\math> for almost every <math> x </math>, or <math> \mu(N) =0< /math>.