real-valued integrands
{"Image DocumentName": "real-valued integrands", "Image ImageDescription": "it\u2019s helpful to have a well-defined integration theory for R-valued integrands: Def(X) = R-valued functions whose graphs are tame (definable in o-minimal) take a riemann-sum approach. \u222b h d\u03c7\u25cf = lim 1/n\u222b floor(nh) d\u03c7. \u222b h d\u03c7\u25cf = lim 1/n\u222b ceil(nh) d\u03c7. unfortunately, \u222b _ d\u03c7 \u25cf & \u222b _ d\u03c7\u25cf are no longer homomorphisms Def(X)\u2192R. however, \u222b _ d\u03c7 \u25cf & \u222b _ d\u03c7\u25cf have an interpretation in o-minimal category. lemma. if h is affine on an open k-simplex, then. h. \u222b h d\u03c7\u25cf = (-1)k inf (h) \u222b h d\u03c7\u25cf = (-1)k sup (h)", "Image XResolution": "37", "Image YResolution": "37", "Image ResolutionUnit": "Pixels/Centimeter", "Image Software": "SlidePlayer", "Image YCbCrPositioning": "Centered"}