Lower Semicontinuous Convex Functions
The theory of convex functions is most powerful in the presence of lower semicontinuity. A key property of lower semicontinuous convex functions is the existence of a continuous affine minorant, which we establish in this chapter by projecting onto the epigraph of the function.
KeywordsConvex Function Measure Space Shannon Entropy Real Hilbert Space Nonempty Closed Convex Subset
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