Finding a Research Paper Which Meaningfully Averages Unbounded Sets

Bharath Krishnan

doi:10.20944/preprints202409.0361.v1

Preprint Concept Paper Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 3 September 2024 / Approved: 4 September 2024 / Online: 4 September 2024 (11:26:09 CEST)

Suppose n ∈ N. We wish to meaningfully average ‘sophisticated’ unbounded sets (i.e., sets with positive n-d Hausdorff measure, in any n-d box of the n-d plane, where the measures don’t equal the area of the boxes). We do this by taking the most generalized, satisfying extension of the expected value, w.r.t the Hausdorff measure in its dimension, on bounded sets which takes finite values only. As of now, I’m unable to solve this due to limited knowledge of advanced math and most people are too busy to help. Therefore, I’m wondering if anyone knows a research paper which solves my doubts.

Expected Values; Sets; Hausdorff measure; Hausdorff dimension; Discretization; Segmentation; Partitions; Samples; Euclidean Distance; Choice Function

Computer Science and Mathematics, Mathematics

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Finding a Research Paper Which Meaningfully Averages Unbounded Sets

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