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A function $f$ is lower semicontinuous iff it is its own lower boundary.

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#real-analysis #solution-verification #semicontinuous-functions
55
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How to prove the criteria for lower semicontinuity of a function at a point?

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#supremum-and-infimum #semicontinuous-functions
46
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Do I have the wrong interpretation of the limit inferior in this definition?

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#limsup-and-liminf #semicontinuous-functions
128
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Definition of Semicontinuity: Confusion in Rudin's RCA

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#real-analysis #measure-theory #continuity #definition #semicontinuous-functions
160
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Upper semicontinuity in real analysis

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#real-analysis #functions #semicontinuous-functions
260
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Convex Functions: Lower Semicontinuity and Epigraph

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#optimization #semicontinuous-functions #non-smooth-optimization
57
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Lower semicontinuity of Lp integral with 0<p<1 with respect to L2 topology

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#functional-analysis #semicontinuous-functions
305
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Checking lower semicontinuity for a function of two variables

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#analysis #optimization #convex-analysis #convex-optimization #semicontinuous-functions
495
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A continuous, convex functional on a Banach space is weakly lower semicontinuous

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#functional-analysis #limsup-and-liminf #semicontinuous-functions
173
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The infimum of a semi-continuous function on a compact set

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#supremum-and-infimum #semicontinuous-functions
36
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Adjoint for real functions

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#real-analysis #lattice-orders #adjoint-functors #semicontinuous-functions
131
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Show that h is lower semicontinuous

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#probability #semicontinuous-functions #large-deviation-theory
72
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Problem 3 chapter 12 Jost Postmodern analysis

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#real-analysis #self-learning #semicontinuous-functions
142
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Is this solution to part of Papa Rudin Chapter 2, Exercise 22 correct?

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#real-analysis #metric-spaces #solution-verification #semicontinuous-functions
76
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Is there any function $f:\mathbb{R} \to \mathbb{R}\cup \{\pm \infty\}$ such that $f$ is lower semi continuous only at $\mathbb{Q}$?

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#real-analysis #semicontinuous-functions

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