Sobolev embeddings, extensions and measure density condition

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Fractional Sobolev extension and imbedding (2014, methodology): “We should point out that the idea to derive the measure density property from the imbedding was originally invented by Haj lasz, Koskela and Tuoninen [13] for Sobolev W 1, -extension domains with p ∈ [1, ∞).”
Measure Density and Extension of Besov and Triebel–Lizorkin Functions (2014, methodology): “The connection of the n-regularity condition, or, in other words, a measure density condition, and the extension property for Sobolev spaces is studied in [39] and in [14].”
Measure density and extendability of Sobolev functions (2008, background): “Our next result, which is an analog of the corresponding result in [10], shows that the existence of a bounded linear extension operator follows from the apparently weaker assumption that each function in the Sobolev class has some extension.”