Version 1
: Received: 3 September 2024 / Approved: 4 September 2024 / Online: 4 September 2024 (11:26:09 CEST)
Version 2
: Received: 7 October 2024 / Approved: 8 October 2024 / Online: 8 October 2024 (16:20:51 CEST)
Version 3
: Received: 14 October 2024 / Approved: 15 October 2024 / Online: 16 October 2024 (09:43:16 CEST)
How to cite:
Krishnan, B. Finding a Research Paper Which Meaningfully Averages Unbounded Sets (v3). Preprints2024, 2024090361. https://doi.org/10.20944/preprints202409.0361.v3
Krishnan, B. Finding a Research Paper Which Meaningfully Averages Unbounded Sets (v3). Preprints 2024, 2024090361. https://doi.org/10.20944/preprints202409.0361.v3
Krishnan, B. Finding a Research Paper Which Meaningfully Averages Unbounded Sets (v3). Preprints2024, 2024090361. https://doi.org/10.20944/preprints202409.0361.v3
APA Style
Krishnan, B. (2024). Finding a Research Paper Which Meaningfully Averages Unbounded Sets (v3). Preprints. https://doi.org/10.20944/preprints202409.0361.v3
Chicago/Turabian Style
Krishnan, B. 2024 "Finding a Research Paper Which Meaningfully Averages Unbounded Sets (v3)" Preprints. https://doi.org/10.20944/preprints202409.0361.v3
Abstract
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. (Unlike previous versions with similar names, we add examples, motivations, and explanations to this version.)
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.