{
  "id": "2002.08986",
  "version": "v1",
  "published": "2020-02-20T19:37:02.000Z",
  "updated": "2020-02-20T19:37:02.000Z",
  "title": "Ergodic Functions That are not Almost Periodic Plus $L^1-$Mean Zero",
  "authors": [
    "Jean Silva"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Ergodic Functions are bounded uniformly continuous $(\\text{BUC})$ functions that are typical realizations of continuous stationary ergodic process. A natural question is whether such functions are always the sum of an almost periodic with an $L^1-$mean zero $\\text{BUC}$ function. The paper answers this question presenting a framework that can provide infinitely many ergodic functions that are not almost periodic plus $L^1-$ mean zero.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-20T19:37:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mean zero",
      "ergodic functions",
      "periodic plus",
      "continuous stationary ergodic process",
      "natural question"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}