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Under what condition does the weak limit of function a function?

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#measure-theory #lebesgue-measure #weak-convergence
126
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How to prove that: $\forall a \in \Bbb R,$ $\|f+a\|_p\ge \frac12\|f\|_p$ when $\int_\Omega f(x)dx= 0$

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#real-analysis #functional-analysis #measure-theory #inequality #lp-spaces
136
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Measure associated with a density multplied by function

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#integration #measure-theory #lebesgue-measure
164
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Use squeeze theorem to integrate over a measurable set $A \subset [-\pi, \pi]$?

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#calculus #limits #measure-theory #definite-integrals #characteristic-functions
714
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Corollary 5 in Royden-Fitzpatrick's Real Analysis: Convergence in Measure

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#real-analysis #measure-theory #proof-explanation
179
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Cumulative distribution function is differentiable at Leb-almost every t

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#probability-theory #measure-theory #lebesgue-measure
56
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Sequence of functions converging to a function

Published on
#integration #measure-theory #convergence-divergence
318
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An integral inequality (Rudin $L^p$-spaces 3.12)

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#functional-analysis #measure-theory #lp-spaces
166
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Characterization of Integrable Functions

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#real-analysis #measure-theory #lebesgue-integral
631
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$f^{-1}([-\infty,r))$ measurable for all rational numbers $r$

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#real-analysis #measure-theory #borel-sets #borel-measures
1k
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differentiability of characteristic function - additional question

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#probability-theory #measure-theory #characteristic-functions
127
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I am not getting this notation

Published on
#measure-theory #dynamical-systems #ergodic-theory
1.3k
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L2 norm of a function w.r.t. its gradient

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#functional-analysis #measure-theory #multivariable-calculus #normed-spaces #sobolev-spaces
69
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Equivalence of the Variation of F$_\mu$(x) and $| \mu |$(($-\infty, x])$

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#real-analysis #measure-theory #signed-measures
4.7k
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Vitali Covering Lemma Proof

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#real-analysis #measure-theory #proof-explanation

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