Gauges of Baire class one functions

Let K be a compact metric space and f :K →R be a bounded Baire class one function. We proved that for any ε > 0 there exists an upper semicontinuous positive function δ of f with finite oscillation index and |f (x) − f (y)| < ε whenever d(x, y) < min{δ(x), δ(y)}. © 2008 Elsevier Inc. All rights reserved.