{"id":"openai-math/Triple-ergodic-averages-with-distinct-integer-slopes","pdf":"https://github.com/openai/math/blob/main/preprints/Triple-ergodic-averages-with-distinct-integer-slopes-October-4-2026/triple-ergodic-distinct-slopes.pdf","url":"https://github.com/openai/math/tree/main/preprints/Triple-ergodic-averages-with-distinct-integer-slopes-October-4-2026","tags":["ergodic-theory","ergodic-averages","dynamics"],"score":0,"title":"Triple ergodic averages with distinct integer slopes","domain":"Dynamical systems and ergodic theory","family":"154","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.DS","summary":"For every invertible mixing probability-preserving transformation, triple ergodic averages of bounded measurable functions along any three pairwise distinct nonzero integer slopes converge almost everywhere to the product of their integrals. The slopes may be positive or negative.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-04","reactions":{},"formalized":false,"family_title":"Pointwise multiple ergodic averages for mixing transformations"}