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Let I ⊂ ℝ be an open interval and let A ⊂ I be any set. Every Baire 1 function f: I → ℝ coincides on A with a function g: I → ℝ which is simultaneously approximately continuous and quasicontinuous if and only if the set A is nowhere dense and of Lebesgue measure zero.
Zbigniew Grande. "On the prolongation of restrictions of Baire 1 functions to functions which are quasicontinuous and approximately continuous." Colloquium Mathematicae 114.2 (2009): 237-243. <http://eudml.org/doc/283424>.
@article{ZbigniewGrande2009, abstract = {Let I ⊂ ℝ be an open interval and let A ⊂ I be any set. Every Baire 1 function f: I → ℝ coincides on A with a function g: I → ℝ which is simultaneously approximately continuous and quasicontinuous if and only if the set A is nowhere dense and of Lebesgue measure zero.}, author = {Zbigniew Grande}, journal = {Colloquium Mathematicae}, keywords = {density topology; approximate continuity; quasicontinuous extension; first Baire class}, language = {eng}, number = {2}, pages = {237-243}, title = {On the prolongation of restrictions of Baire 1 functions to functions which are quasicontinuous and approximately continuous}, url = {http://eudml.org/doc/283424}, volume = {114}, year = {2009}, }
TY - JOUR AU - Zbigniew Grande TI - On the prolongation of restrictions of Baire 1 functions to functions which are quasicontinuous and approximately continuous JO - Colloquium Mathematicae PY - 2009 VL - 114 IS - 2 SP - 237 EP - 243 AB - Let I ⊂ ℝ be an open interval and let A ⊂ I be any set. Every Baire 1 function f: I → ℝ coincides on A with a function g: I → ℝ which is simultaneously approximately continuous and quasicontinuous if and only if the set A is nowhere dense and of Lebesgue measure zero. LA - eng KW - density topology; approximate continuity; quasicontinuous extension; first Baire class UR - http://eudml.org/doc/283424 ER -