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    "title": "Remez sharp polynomial bound from control on a subset of prescribed measure",
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        "title": "Sur une propriété extrémale des polynomes de Tchebychef, Kharkoff series4t13fasc1(1936)93–95",
        "url": "https://www.math.auckland.ac.nz/hat/fpapers/remezppr.pdf",
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            "citation": "Sur une propriété extrémale des polynomes de Tchebychef, Kharkoff series4t13fasc1(1936)93–95",
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        "description": "One-dimensional real polynomial and Lebesgue-measure control, not a general measurable-function, multivariate or arbitrary-set inequality with the same constant. Degree n>=1 and k>0; n=0 is trivial and not included in an extremizer-uniqueness claim. The source's footnote links earlier approximation algorithms, which are not separately claimed as established by this inequality paper. One-dimensional Lebesgue-measure statement, not arbitrary functions or unchanged multivariate constants. Positive k,0<theta<1; constant-polynomial case does not inherit a uniqueness-of-extremizer assertion. Kiev byline retained without present-day-country guess.",
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          "citation": "Sur une propriété extrémale des polynomes de Tchebychef, Kharkoff series4t13fasc1(1936)93–95",
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      "statement": "# Remez sharp polynomial bound from control on a subset of prescribed measure\n\nFor a real polynomial p of degree at most n, bounded by k on a measurable subset E of an interval S of length l with measure at least lambda=theta*l, 0<theta<1, the interval supremum is at most k*T_n(2/theta-1). Shifted Chebyshev polynomials on an endpoint interval of length lambda attain the bound.\n\n## Scientific scope\n\nOne-dimensional real polynomial and Lebesgue-measure control, not a general measurable-function, multivariate or arbitrary-set inequality with the same constant. Degree n>=1 and k>0; n=0 is trivial and not included in an extremizer-uniqueness claim. The source's footnote links earlier approximation algorithms, which are not separately claimed as established by this inequality paper. One-dimensional Lebesgue-measure statement, not arbitrary functions or unchanged multivariate constants. Positive k,0<theta<1; constant-polynomial case does not inherit a uniqueness-of-extremizer assertion. Kiev byline retained without present-day-country guess.\n\n## Reading status\n\nThis is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.\n\n## People and systems\n\nEugène Remes\n\nSource-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.\n\n\n\n## Original sources\n\n- [Sur une propriété extrémale des polynomes de Tchebychef, Kharkoff series4t13fasc1(1936)93–95](https://www.math.auckland.ac.nz/hat/fpapers/remezppr.pdf)\n",
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      "title": "Remez sharp polynomial bound from control on a subset of prescribed measure"
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    "id": "remez-sharp-polynomial-measure-subset-inequality-1936",
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    "revision": 1,
    "title": "Remez sharp polynomial bound from control on a subset of prescribed measure",
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    "what_changed": "For a real polynomial p of degree at most n, bounded by k on a measurable subset E of an interval S of length l with measure at least lambda=theta*l, 0<theta<1, the interval supremum is at most k*T_n(2/theta-1). Shifted Chebyshev polynomials on an endpoint interval of length lambda attain the bound.",
    "scope": "For a real polynomial p of degree at most n, bounded by k on a measurable subset E of an interval S of length l with measure at least lambda=theta*l, 0<theta<1, the interval supremum is at most k*T_n(2/theta-1). Shifted Chebyshev polynomials on an endpoint interval of length lambda attain the bound. One-dimensional real polynomial and Lebesgue-measure control, not a general measurable-function, multivariate or arbitrary-set inequality with the same constant. Degree n>=1 and k>0; n=0 is trivial and not included in an extremizer-uniqueness claim. The source's footnote links earlier approximation algorithms, which are not separately claimed as established by this inequality paper. One-dimensional Lebesgue-measure statement, not arbitrary functions or unchanged multivariate constants. Positive k,0<theta<1; constant-polynomial case does not inherit a uniqueness-of-extremizer assertion. Kiev byline retained without present-day-country guess.",
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