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Bounded sequence in $L^\infty$ which converges in $L^1$

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#functional-analysis #lp-spaces #weak-convergence #strong-convergence
48
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Boundedness and Strong convergence

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#functional-analysis #hilbert-spaces #weak-convergence #strong-convergence
44
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Does this conclude that $ \int_E f_jg_j dx \to \int_E fgdx$?

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#measure-theory #weak-convergence #strong-convergence
221
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Almost sure convergence of quadratic form x'Ax

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#probability-theory #convergence-divergence #probability-limit-theorems #strong-convergence
71
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Weak and strong convergence of operator sequence

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#functional-analysis #operator-theory #weak-convergence #strong-convergence
269
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Example that strong convergence does not imply convergence in norm

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#convergence-divergence #strong-convergence
90
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On a sequence $f_k$ in $L^{2+\frac{1}{k}}$

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#banach-spaces #lp-spaces #weak-convergence #strong-convergence
148
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About weak convergence and convergence of norms

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#functional-analysis #weak-convergence #strong-convergence
111
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Poke holes in this proof of the SLLN

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#law-of-large-numbers #strong-convergence
46
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Operator satisfying certain properties

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#functional-analysis #operator-theory #compact-operators #strong-convergence
71
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Weak, Strong, a.e. convergence parameters in $L^2(R^3)$ excercise

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#functional-analysis #lp-spaces #weak-convergence #strong-convergence
55
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Laws of large numbers problem: Convergence of a symmetric sequence

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#probability-theory #law-of-large-numbers #strong-convergence
161
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Does weak convergence imply strong convergence for parameterized measure?

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#measure-theory #weak-convergence #strong-convergence
36
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If $H$ is Hilbert and $T\in B(H)$ is left shift w.r.t. the OB $(e_{k})_{k\in\mathbb{N}}$, then $T^{n}x\to0$ for all $x\in H$

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#sequences-and-series #functional-analysis #hilbert-spaces #orthonormal #strong-convergence
35
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Range of strong limit of a semigroup belongs to the fixed space?

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#functional-analysis #operator-theory #semigroup-of-operators #strong-convergence

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