Almost everywhere first-return recovery

• Autorzy: Evans M. J. , Humke P. D.
• Języki publikacji: EN

Abstrakty

EN

We present a new characterization of Lebesgue measurable functions; namely, a function f : [0,1] --> R is measurable if and only if it is first-return recoverable almost everywhere. This result is established by demonstrating a connection between almost everywhere first-return recovery and a first-return process for yielding the integral of a measurable function.

Słowa kluczowe

EN

Lebesgue measurable functions; first-return recovery

PL

funkcja mierzalna Lebesque

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2004
• Tom: Vol. 52, nr 2
• Strony: 185--195
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Evans M. J.

• Department of Mathematics, Washington and Lee University, Lexington, VA 24450, U.S.A.

autor

Humke P. D.

• Department of Mathematics, St. Olaf College, Northfield, MN 45701, U.S.A.

Bibliografia

• [1] U. B. Darji and M. J. Evans, Recovering Baire 1 functions, Mathematika 42 (1995), 43-48.
• [2] -, -, A first return examination of the Lebesgue integral, Real Anal. Exchange 27 (2001/2002), 573-581.
• [3] U. B. Darji, M. J. Evans, C. Freiling, and R. J. O'Malley, Fine properties of Baire one functions, Fund. Math. 155 (1998), 177-188.
• [4] U. B. Darji, M. J. Evans, and R. J. O'Malley, First return path systems: differentiability, continuity, and orderings, Acta Math. Hungar. 66 (1995), 83-103.
• [5] -, -, -, A first return characterization for Baire 1 functions, Real Anal. Exchange 19 (1993/94), 510-515.
• [6] C. Kuratowski, Topologie, Vol. 1 , 4th ed., Monograf. Mat. 20, PWN, Warszawa, 1958.
• [7] J. C. Oxtoby, Measure and Category. A Survey of the Analogies Between Topological and Measure Spaces, 2nd ed., Grad. Texts in Math. 2, Springer, New York, 1980.