These three muscles act as flexors at the elbow joint.
The extensor carpi radialis brevis and longus are both weak flexors at the elbow joint. Brevis moves the arm from ulnar abduction to its mid-position and flexes dorsally. Longus is a weak pronator in the flexed arm and a supinator in the outstretched arm. At the carpal joints longus acts in dorsiflexion with the extensor carpi ulnaris and in radial abduction with the flexor carpi radialis. These two muscles are called "fist clenchers" because they must be slightly flexed dorsally during clenching to permit maximal flexion.
Brachoradialis is inserted distally on the radius end therefore, unlike the previous two muscles, only acts on the forearm. It brings the forearm into midposition between supination and pronation, and in this position it acts as a flexor. In slow movements and in the supinated forearm it has a minimal flexor action.
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... For instance, a sequence of functions can frequently be constructed that approximate, in a suitable sense, the solution to a problem ... Then the integral of the solution function should be the limit of the integrals of the approximations ... However, many functions that can be obtained as limits are not Riemann integrable, and so such limit theorems do not hold with the Riemann integral ...
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