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Duly

adverb

/ˈduːli/

Meaning

in accordance with what is required or appropriate; at the proper time

The documents were duly signed and submitted.

properly, appropriately, correctly

improperly, inappropriately, incorrectly

duly noted, duly signed, duly authorized

without making careful distinctions; randomly; without discrimination

in a confidential manner; secretly; privately

in any case; regardless of other considerations

without preparation; spontaneously; improvised

to a higher degree than is usual or expected

At a rapidly increasing rate; growing or expanding very quickly and intensely.