I am aware that using the counting measure on Lebesgue you can get important results. I am wondering if there is a way to exchange the limits using Dominated Convergence Theorem.Let a n , m be indexed from 0 to infinity. | a n , m | &lt; M for all indexes. lim m → ∞ a n , m exists for all m.Does DCT allow you do say lim n → ∞ lim m → ∞ a n , m = lim m → ∞ lim n → ∞ a n , m

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I am aware that using the counting measure on Lebesgue you can get important results. I am wondering if there is a way to exchange the limits using Dominated Convergence Theorem.Let       a          n      ,      m       be indexed from 0 to infinity.       |        a          n      ,      m            |    &amp;lt;  M for all indexes.       lim          m      →      ∞            a          n      ,      m       exists for all m.Does DCT allow you do say       lim          n      →      ∞            lim          m      →      ∞            a          n      ,      m        =      lim          m      →      ∞            lim          n      →      ∞            a          n      ,      m

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I am aware that using the counting measure on Lebesgue you can get important results. I am wondering

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