Let f and g be measurable functions on E.
(a) If f and g are finite almost everywhere in E, show that f + g is measurable no matter how we define it at the points when it has the form +[infinity] or -[infinity].
(b) Show that fg is measurable without restriction on the finiteness of f and g.
Show that f + g is measurable if it is defined to have the same value at every point where it has the form +[infinity] or -[infinity].
Note that a function h defined on E is measurable if and only if both (h+[infinity]) and (h-[infinity]) are measurable, and the restriction of h to the subset of E where h is finite is measurable.